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SUMMARY TECHNICAL REPORT 
OF THE 

NATIONAL DEFENSE RESEARCH COAIMITTEE 


This document contains information affecting the national defense of the 
United States within the meaning of the Espionage Act, 50 U. S. C., 31 and 32, 
as amended. Its transmission or the revelation of its contents in any manner 
to an unauthorized person is prohibited b}' law. 

This volume is classified CONFIDENTIAL in accordance with security regula¬ 
tions of the War and Navy Departments because certain chapters contain 
material which was CONFIDENTIAL at the date of printing. Other chapters 
may have had a lower classification or none. The reader is advised to consult 
the War and Navy agencies listed on the reverse of this ])age for the current 
classification of any material. 


CONFIDENTIAL 


Manuscript and illustrations for this v'olume were prepared for 
publication by the Summary Reports Groups of the C’olumbia 
University Division of War Research under contract OEMsr-1131 
with the Office of Scientific Research and Development. This vol¬ 
ume was printed and bound by the Columbia University Press. 

Distribution of the Summary Technical Report of NDRC has been 
made by the War and Navy Departments. Inquiries concerning the 
availability and distribution of the Summary Technical Report 
volumes and microfilmed and other reference material should be 
addressed to the War Department Library, Room lA-522, The 
Pentagon, Washington 25, D. C., or to the Office of Naval Re¬ 
search, Navy Department, Attention: Reports and Documents 
Section, Washington 25, D. C. 


Copy No. 

147 


This volume, like the seventy others of the Summary Technical 
Report of NDRC, has been written, edited, and printed under 
great pressure. Inevitably there are errors which have slipped past 
Division readers and proofreaders. There may be errors of fact not 
known at time of printing. The author has not been able to follow 
through his writing to the final page proof. 

Please report errors to: 

JOINT RESE.\RCH AND DEVELOPMENT BOARD 
PROGRAMS DIVISION (STR ERRATA) 

WASHINGTON 25 , D. C. 

A master errata sheet will be compiled from these reports and sent 
to recipients of the volume. Your help will make this book more 
useful to other readers and will be of great value in preparing any 
revisions. 


CONFIDENTIAL 


SUMMARY TECHNICAL REPORT OF DIVISION 6, NDRC 

VOLUME 13 


THE 

DESIGN AND CONSTRUCTION 
OF MAGNETOSTRICTION 
TRANSDUCERS 


OFFICE OF SCIENTIFIC RESEARCH AND DEVELOPMENT 

V ANNE VAR BUSH, DIRECTOR 

NATIONAL DEFENSE RESEARCH COMMITTEE 
JAMES B. CON A NT, CHAIRMAN 

DIVISION 6 
JOHN T. TATE, CHIEF 


WASHINGTON, D. C., 1946 


CONFIDENTIAL 



NATIONAL DEFENSE RESEARCH COMMITTEE 


James B. C'onant, Chairman 
Richard C. Tolman, Vice Chairman 
Roger Adams Army Representative ' 

Frank B. Jewett Navy Representative - 

Karl T. Compton Commissioner of Patents * 

Irvin Stewart, Executive Secretary 


'Army representatives in order of service: 


Maj. Gen. G. V. Strong 
Maj. Gen. R. C. Moore 
Maj. Gen. C. C. Williams 
Brig. Gen. W. .\. Wood, Jr. 

Got PI 


Col. L. A. Denson 
Col. P. R. P^aymonville 
Brig. Gen. E. A. Regnier 
Col. M. M. Irvine 
A. Roiitheau 


Wary representatives in order of service: 

Rear .\dni. H. G. Bowen Rear Adin. J. A. P’urer 

Capt. Lyhrand P. Smith Rear .\dm. A. H. Van Keuren 

Commodore H. A. Schade 
" Commissioners of Patents in order of service: 

Conway P. Coe Casper W. Ooms 


NOTES ON THE ORGANIZATION OF NDRC 


The duties of the National Defense Research Committee 
were (1) to recommend to the Director of OSRD suitable 
projects and research programs on the instrumentalities of 
warfare, together with contract facilities for carrying out 
these projects and programs, and (2) to administer the tech¬ 
nical and scientific work of the contracts. More specifically, 
NDRC functioned by initiating re.search projects on re¬ 
quests from the Army or the Navy, or on requests from an 
allied government transmitted through the Liaison Office 
of OSRD, or on its own considered initiative as a result of 
the experience of its membei-s. Proposals prepared by the 
Division, Panel, or Committee for research contracts for 
performance of the work involved in such projects were 
first reviewed by NDRC, and if approved, recommended to 
the Director of OSRD. P'pon approval of a proposal by the 
Director, a contract permitting maximum flexibility of 
scientific effoi't was arranged. The business aspects of the 
contract, including such matters as materials, clearances, 
vouchers, patents, joriorities, legal matteis, and administra¬ 
tion of patent matters were handled by the PNecutive Sec¬ 
retary of OSRD. 

Originally NDRC administered its work through five 
divisions, each headed by one of the NDRC members. 
These were: 

Division — .\rmor and Ordnance 
Division B — Bombs, Fuels, Gases, & Problems 
Division C — Communication and Transportation 
Division D — Detection, Controls, and Instruments 
Division PI — Patents and Inventions 


In a reorganization in the fall of 1942, twenty-three ad¬ 
ministrative divisions, panels, or committees were created, 
each with a chief selected on the basis of his outstanding 
work in the particular field. The NDRC members then be¬ 
came a reviewing and advisory group to the Director of 
OSRD. The final organization was as follows: 

Division 1 — Ballistic Research 

Division 2 — PIffects of Impact and Explosion 

Division 3 — Rocket Ordnance 

Division 4 — Ordnance Accessories 

Division 5 — New Missiles 

Division 6 — Sub-Surface Warfare 

Division 7 — Fire Control 

Division 8 — Explosives 

Division 9 — Chemistry 

Division 10 — Absorbents and Aerosols 

Division 11 — Chemical PIngineering 

Division 12 — Transportation 

Division 13 — Electrical Communication 

Division 14 — Radar 

Division 15 — Radio Coordination 

Division 16 — Optics and Camouflage 

Division 17 — Physics 

Division 18 — War Metallurgy 

Division 19— Miscellaneous 

.Applied Mathematics Panel 

.Applied Psychology Panel 

Committee on Propagation 

Tropical Deterioration .\dministrative Committee 


('ONFIDENTIAL Library of Congress 



201.5 


4909.57 















NDRC FOREWORD 


4 s EVENTS of the years preceding 1940 revealed 
more and more clearly the seriousness of the 
world situation, many scientists in this country came 
to realize the need of organizing scientific research for 
service in a national emergency. Recommendations 
which they made to the White House were given care¬ 
ful and sympathetic attention, and as a re.sult the 
National Defense Research Committee [NDRC] was 
formed by Executive Order of the President in the 
summer of 1940. The members of NDRC, appointed 
by the President, were instructed to supplement the 
work of the Army and the Navy in the development 
of the instrumentalities of war. A year later, upon 
the e.stablishment of the Office of Scientific Research 
and Development [OSRD], NDRC became one of 
its units. 

The Summary Technical Report of NDRC is a 
conscientious effort on the part of NDRC to sum¬ 
marize and evaluate its work and to present it in a 
useful and permanent form. It comprises some 
seventy volumes broken into groups corresponding 
to the NDRC Divisions, Panels, and Committees. 

The Summary Technical Report of each Division, 
Panel, or Committee is an integral survey of the work 
of that grouj). The first volume of each group’s re¬ 
port contains a .summary of the report, stating the 
problems pre.sented and the philosophy of attacking 
them and .summarizing the re.sults of the research, de¬ 
velopment, and training activities undertaken. Some 
volumes may be “state of the art” treatises covering 
subjects to which various research groups have con¬ 
tributed information. Others may contain de,scrip- 
tions of devices developed in the laboratories. A 
master index of all these divisional, panel, and com¬ 
mittee reports which together constitute the Sum¬ 
mary Technical Report of NDRC is contained in a 
separate volume, which also includes the index of a 
microfilm record of pertinent technical laboratory 
reports and reference material. 

Some of the NDRC-sponsored re.searches which 
had been declassified by the end of 1945 were of 
sufficient popular interest that it was found desirable 
to report them in the form of monographs, such as 
the .series on radar by Division 14 and the monograph 
on sampling inspection by the Applied Mathematics 
Panel. Since the material treated in them is not dupli¬ 


cated in the Summary Technical Report of NDRC, 
the monographs are an important part of the story 
of the.se aspects of NDRC research. 

In contrast to the information on radar, which is 
of widespread interest and much of which is released 
to the public, the research on subsurface warfare is 
largely cla.ssified and is of general interest to a more 
restricted group. As a con.secpience, the report of 
Division 6 is found almost entirely in its Summary 
Technical Report, which runs to over twenty volumes. 
The extent of the work of a Division cannot therefore 
be judged solely by the number of volumes devoted 
to it in the Summary Technical Report of NDRC: 
account must be taken of the monographs and avail¬ 
able reports published elsewhere. 

Any great cooperative endeavor must stand or fall 
with the will and integrity of the men engaged in it. 
This fact held true for NDRC from its inception, and 
for Division 6 under the leadership of Dr. John T. 
Tate. To Dr. Tate and the men who worked with 
him — .some as members of Division 6, .some as 
representatives of the Division’s contractors — be¬ 
longs the sincere gratitude of the Nation for a diffi¬ 
cult and often dangerous job well done. Their efforts 
contributed significantly to the outcome of our naval 
operations during the war and richly deserved the 
warm response they received from the Nav^^ In ad¬ 
dition, their contributions to the knowledge of the 
ocean and to the art of oceanographic research will 
as.suredly speed peacetime investigations in this field 
and bring rich benefits to all mankind. 

The Summary Technical Report of Division 6, 
prepared under the direction of the Division Chief 
and authorized by him for publication, not only 
presents the methods and residts of wddely varied re¬ 
search and development programs but is essentially a 
record of the unstinted loyal cooperation of able men 
linked in a common effort to contribute to the defense 
of their Nation. To them all we extend our deep 
appreciation. 

VAnnevar Bush, Director 
Office of Scientific Research and Development 

J. B. CoNANT, Chairman 
National Defense Research Committee 


CONFIDENTIAL 






FOREWORD 


4s PART OF the broad Division G program of re- 
-L^search and development in underwater sound, a 
fundamental investigation of the pi’operties and be¬ 
havior of “hydroacoustic generators and receivers,” 
more commonly called transducers, was undertaken. 
It seemed desirable that the West Coast laboratory 
should pretty largely concern itself with devices 
based upon piezo-electric effect of certain crystals, 
while the Harvard laboratory should concern itself 
with devices employing the magnetostriction effect, 
most markedly shown by nickel, iron, and their 
alloys. 

The research and development work performed at 
the West Coast Laboratory at San Diego under a con¬ 
tract with the University of California Division of 
War Research, including some reference to work by 
other agencies, is described in Volume 12 of this se¬ 
ries. This present report, prepared in large part by 
Paul E. Sabine of the staff of the Harvard Under¬ 
water Sound Laboratory, presents not only the work 
of the Harvard Laboratory, but also to some extent 
the work in this same field of other research organ¬ 
izations. While it is not possible accurately to fore¬ 
cast the future requirements of the military, it is very 
certain that the subject here presented will continue 
to be of most substantial interest, and it is hoped this 
material will be helpful primarily to those who may 


be concerned with further research and development 
relating to structures for generating or detecting un¬ 
derwater sounds. 

The Division owes its thanks to Sabine, F. P. 
Bundy, and others of the Harvard staff for their will¬ 
ingness to undertake preparation of this volume. The 
Division also acknowledges its indebtedness to E. M. 
Wise and the International Nickel Company. Wise, 
acting as consultant to Division 6, was ever ready to 
furnish information to the contractors of the Division 
and to assist in every way in the obtaining of mate¬ 
rials for test. As to Navy liaison the portion of this re¬ 
search and development activity performed by Divi¬ 
sion 6 was not set up as a formal Navy-NDRC proj¬ 
ect, and consequently no formal appointment of 
Navy liaison was made. However, because this work 
was basic to other formal Navy-NDRC projects, cer¬ 
tain Navy officers assigned to these projects were 
kept fully informed as to progress and plans. Among 
these were Captain Rawson Bennett, Jr. and Com¬ 
mander J. C. iMyers of the Bureau of Ships, who 
recognized the importance of the subject and gave it 
their most cordial support. 

John T. Tate 
Chief, Division 6 


CONFIDENTIAL 








PREFACE 


T he work on magnetostriction transducers at 
Harvard Underwater Sound Lahoratory[HUSL] 
grew out of the necessity of providing adequate elec¬ 
tro-acoustic devices designed to meet the specific re¬ 
quirements of the various projects on which otlier 
groups in the laboratory were engaged. Initially, de¬ 
signing and building the requisite transducer for anj' 
project was a part of the job of the special group to 
which the project was assigned. It soon became ap¬ 
parent that this arrangement involved duplication of 
effort and was not adding materially to the fund of 
general knowledge on the subject of transducer de¬ 
sign and performance. 

In August 1942 a special tran.sducer and measure¬ 
ment group was set up, the functions of which were 
(I) to carry on fundamental studies on magnetostric- 
tive properties of materials, (2) to develop general 
types of transducers, (3) to design and build special 
transducers required by other groups, (4) to develop 
and improve equipment for making electrical and 
acoustical measurements on transducers, and (5) to 
assume the responsibility for all such measurements 
required by the different groups in the laboratory. 

Attention at HUSL naturally centered almost ex¬ 
clusively on magnetostriction devices, since it was at 
Harvard that the pioneer work in this field by G. W. 
Pierce and his co-workers was done. Very early in 
the program Pierce generously turned over to this 
laboratory his original research notes on supersonic 
magnetostrictive vibrators. Material in these notes 
furnished the basic ideas on which many of the earlier 
experimental forms were constructed. 

At the outset, very little theoretical material on the 
dynamics of magnetostrictive vibrators was avail¬ 
able. A paper by Butterworth and Smith, published 
in 1931, and a comprehensive report by Smith to the 
British Admiralty comprised about all the published 
matter that had immediate bearing on the specific 
problem. 

The work of the Theory Group at HUSL has been 
throughout closely coordinated with the experimen¬ 
tal work of the Transducer Group. In June 1943, a 
report from the Theory Group was circulated under 
the title Magnetostrictive Transducers. A year earlier, 
a report titled Directivity Patterns had issued from 
the same source. The subject matter of these two re¬ 
ports, expanded and revised, constitutes a substantial 
portion of the present text. 


The results of work by other laboratories in this 
field have been included. Grateful acknowledgment 
is made to the staffs of the Naval Re.search Labora¬ 
tory at Anacostia, of the Columbia Univensity Divi¬ 
sion of War Research at the U. S. Navy Underwater 
Sound Laboratory at New London, and of the Bell 
Telephone Laboratories, for material which they 
have supplied. Thanks also are due to the Submarine 
Signal Company for detailed information on QC' pro¬ 
jectors of their manufacture. 

The correct appraisal of transducer performance 
can only be based on the results of acoustical and 
electrical measurements. The recognition of the need 
for improved mea.suring equipment and technique 
over the crude methods originally employed has led 
to an appreciable increase in the precision of both 
acoustical and electrical measurements. In view of 
the e.soteric nature of the field, it has seemed worth¬ 
while to gi\’e a fairly detailed account of the equip¬ 
ment and methods that have been developed at the 
two open-water stations of the Harvard Laboratory. 
The .same reason is given as warrant for the inclusion 
of the account of impedance and admittance bridge 
mea.surements. The.se measurements have proved an 
extremely useful means both of studying transducers 
in the developmental stage, and of properly as-sem- 
bling multielement units for optimum performance. 

The material presented herein has been prepared 
with a twofold purpose in mind: first, to give a coher¬ 
ent account of the efforts of a fairly large group of 
workers in an untried field, and .second, at the .same 
time to provide a .source of information for the guid¬ 
ance of those who hereafter may be called on to carry 
forward a far-from-completed task. In carrying out 
the latter, it seemed useful to report some of our 
mistakes. Space limitations preclude the recording of 
all of them. The work of preparation is the joint effort 
of a number of writers, who, for the most part, have 
worked under the handicap of time limits and the 
pressure of other duties. The lack of uniformity in 
style and treatment will be all too evident. While it 
has been the editorial aim to .sandpaper the joints 
and to eliminate repetition, it has been impossible to 
do this completely without an amount of rewriting 
which would exceed the time allotted to the job. 

Thought has been given to the order of pre.senta- 
tion of the various subjects. The three purely theo¬ 
retical chapters as well as a chapter on fundamental 

ix 


CONFIDENTIAL 


PREFACE 


research on the magnetic and magnetostrictive prop¬ 
erties of materials may seem a somewhat formidable 
barrier to the reader concerned with the immediate 
job of building a successful magnetostriction trans¬ 
ducer. However, the frequent references in the later 
text to the theoretically derived relations, and the use 
of these relations in practical design problems, made 
the inclusion of this material in the early portion of 
the report seem necessary even if not inviting. 

Possibly a disproportionate amount of space has 
been devoted to the minutiae of transducer manufac¬ 
ture. However, many of these details had to be 


learned the hard way and experience has emphasized 
the fact that the difference between success and fail¬ 
ure in achieving a desired type of vibration in a com¬ 
plicated structure may be a matter of many small 
and unforeseen factors. We have tried to err on the 
side of too much rather than too little detail. 

We cherish no illusion of having covered our sub¬ 
ject completely. We hope only that this record of our 
efforts will give future workers in the field the benefits 
of our successes and spare them the embarrassment of 
repeating our failures. 

Paul E. Sabine 


CONFIDENTIAL 



CONTENTS 

CHAPTER page 

1 Introduction. 1 

2 Transducers as Multiterminal Networks.22 

3 Magnetostrictive Vibrators and Equivalent Circuits . . 35 

4 Magnetic and Magnetostrictive Properties of Materials . 62 

5 Directivity Patterns.105 

6 Radially Vibrating Transducers.139 

7 Longitudinally Vibrating Laminated Stacks.176 

8 Tube-and-Plate Transducers.223 

9 Measurement of Electrical Characteristics.237 

10 Open-Water Measurement at HUSL.288 

11 High Power Driving of Magnetostrictive Transducers . . 323 

12 Future Developments.356 

13 Theory and Design of Magnetostriction Scanning Sonar 

Transducers.365 

14 Construction and Testing of Scanning Transducers . . . 423 

. Glossary.451 

Bibliography.455 

Contract Numbers.477 

Index.479 


CONFIDENTIAL 





















Chapter 1 

INTUODUCTION 


Among the many devices that have been proposed 
and used for producing and detecting acoustic waves 
in water, two tj’pes have proved to be most effective. 
The first type employs the piezoelectric properties 
of crystals for electroacoustic tran.sformation of 
energy. The second operates by virtue of the mag- 
netostrictive properties of ferromagnetic materials. 
The magnetization of a specimen of such material 
involves certain changes in its internal structure 
which set up stresses in the specimen and minute 
changes in its physical dimensions. The phenomena 
associated with these changes are known under the 
general term magnetostriction. According to gen¬ 
erally accepted theory, a ferromagnetic material is 
made up of elementary “domains,” regions through¬ 
out which the inherent magnetization is unidirec¬ 
tional. In the unmagnetized state, the magnetization 
of the domains is oriented in random fashion with 
reference to each other, so that their resultant mag¬ 
netic moment is nil. Under the action of an imposed 
magnetic field there is an alignment of the mag¬ 
netization of the domains in the direction of the 
applied field, with resultant internal stre.s.ses and 
strains. The effect, in any particular case, is a.s.so- 
ciated with the molecular, crystalline, and grain 
structure of the metal in question, and the magneto- 
strictive forces developed in a body under restraint 
are accordingly very great. 

Although a detailed theoretical treatment of the 
phenomenon is outside the immediate purpose of 
this book, an elementary account of the mechanics of 
magnetostrictive action and the relation of magneto- 
strictive properties to the other magnetic properties 
of metals and alloys may serve as a useful background 
for a more detailed presentation later. 

1.1 FUNDAMENTAL MAGNETIC 
RELATION.S — STEADY STATE 


rection at any point correspond to those of the force 
on an idealized unit North magnetic pole at that 
point. 

For the purpose of illustration and definition of 
terms, the familiar laboratory experiment is u.sed of 
measuring by the ballistic method the magnetization 
of a sample of ferromagnetic material, such as nickel. 
For simplicity, the magnetizing field is as.sumed to 
be set up inside a long solenoid by a direct current 
i flowing through the windings, and the solenoid and 
the nickel core are taken to be long enough so that 
the effect of the free poles induced at the two ends is 
negligible. Without the core, the uniform field in 
oersteds within the .solenoid is given by the familiar 
equation 

// = 47rm, (1) 


where n is the number of turns of the windings per 
unit length and i the current in abamperes. 

Suppose that without the core a thin secondary or 
search coil of /q turns enclosing an area of A, sq cm 
be placed at the midpoint of the solenoid, and that 
the terminals of the coil be connected to a ballistic 
galvanometer. The total magnetic flux (maxwells) 
through the search coil is A,B = B is the 

flux density (gauss), sometimes called the “mag¬ 
netic induction,” and n is the magnetic permeability 
of the core material. For air, y is a constant and 
approximately equal to unity. For ferromagnetic 
materials y is a function of //, and for any assigned 
value of H, the value of y will depend upon the 
temperature and the previous history of the sample. 

By Faraday’s law, the emf in abvolts generated 
in the search coil by varying the normal component 
of the magnetic flux through it is given by the 
eciuation 


5<I> dB 

(s = —Os— = —UsAs— 

dt dt 


— OsAs 


dt 


(2) 


The concept of the magnetic field of force is funda¬ 
mental in electromagnetic theory. Such a field exists 
in the neighborhood of permanent magnets and of 
conductors carrying electric currents. It is repre¬ 
sented by a space vector whose magnitude and di¬ 


Equation (2) will serve to define 4>, B, and y. 

The search coil and the ballistic galvanometer 
constitute a flux meter, since by an easy analysis it 
can be shown that the throw 0 of the galvanometer, 
produced by a sudden change in the magnetic 


CONFIDENTIAL 



2 


INTRODUCTION 


flux through the search coil, is proportional to that 
change. Hence 

0 = = aMnH), (3) 

where a is a proportionality constant involving the 
area, the number of turns of the search coil, and the 
total resistance of the search-coil circuit. 

If a step-by-step increase is made in the current 
in the primary windings of the solenoid with an air 
core, then, since m for air is a constant, the cumulative 
throws of the ballistic galvanometer will increase 
linearly with the current. With a ferromagnetic 
nickel core, however, the results are quite different. 
Under the action of the magnetizing field, there will 
be a reorientation of the magnetic fields of the 


is zero, I is zero — that is, if the specimen is initially 
unmagnetized — then for any value of H, 

B = H + iwl = fiH, 

I 

H 

and K is called the susceptibility of the ferromagnetic 
material. 

In Figure 1 the solid line is the magnetization curve 
for commercial A-nickel annealed at a temperature of 
1000 C in air. Initially the specimen was in the 
demagnetized state. The magnetizing field was in¬ 
creased from zero in definite steps, with a number 
of reversals of the field at each step. Each plotted 



-10 0 20 40 60 80 100 120 140 160 

H IN OERSTPnc 

Figure 1 . Magnetization and hysteresis of annealed .\-nickel. 


domains, with a resultant increase in the magnetic 
moment of the core. Assume that the search coil 
occupies the same position as formerly but lies in a 
narrow transverse slot cut in the core. Then the 
increment in the flux through the coil resulting from 
an increase in H will include also a term due to the 
increase in the induced magnetization. If it is 
assumed that the sample is uniformly magnetized 
and if the magnetic moment per unit volume is de¬ 
noted by I, then the contribution of the induced 
magnetization to the flux density through the search 
coil is 47r/. Hence, for an increment \H in the 
magnetizing field, the increment in B is given by the 
equation Afi = A(// -|- drr/) = If when H 


point represents the final constant value of B, at¬ 
tained after a series of reversals. Such a curve is 
referred to as the “normal magnetization curve.’’ 

To clarify further the meaning of our terms, sup¬ 
pose a very narrow slot is cut across a sample of ferro¬ 
magnetic material in a magnetic field (Figure 2). 
There will be in the .slot a flux density H due to field. 
Free poles of strength I per unit area will be induced 
on the free faces of the slot. The flux density across 
the slot due to these poles will be iwl. The total 
flux density is then H + 4x7. If, instead of the 
transverse slot, a long needle-like slot is parallel to 
the field, then the contribution of the induced mag¬ 
netization to the flux density at the measuring point 


CONFIDENTIAL 




















































STATIC MAGNETOSTRICTION — HISTORICAL 


3 


within this slot will be negligible, and the measured 
flux density will be // alone. It is to be noted that 
B, H, and 4x7 are all quantities of the same kind and 
are expressible in the same units. But it is con¬ 
venient — particularly in the case of the magnetic 




Figure 2. The relation B = H + Awl. 


circuit — to think of the flux as analogous to current 
and the field as a magnetomotive force correspond¬ 
ing to emf in the electric circuit. Hence H and B 
are quantities of the same kind, but for convenience 
are expressed in different units, the first in oersteds, 
the second in gauss. 

In the preceding paragraphs, the various relations 
have been based on the fundamental laws of elec¬ 
tromagnetism. The equations given hold only when 
the quantities involved are in absolute electromag¬ 
netic units. Table 1 gives the numerical relation 
between the practical and the electromagnetic units. 


Table 1 


Quantity 

Symbol 

Practical 

unit 

Value 
in emu 

14ectric charge 

Q 

coulomb 

10-' 

Electromotive force (and 

e 

volt 

10* 

electric potential) 




Capacity 

c 

farad 

10-» 

Current 

i 

ampere 

10-' 

Resistance 

R 

ohm 

10* 

Inductance 

L 

henry 

10* 

Magnetic pole strength 

m 


1 

Magnetic field strength 

H 

oersted 

1 

Intensity of magnetization 

I 


1 

Magnetic induction 1 




Flux density / 




Magnetic flux 


maxwell 

1 


Various systems of units are employed in practice, 
but unless otherwise indicated the practical units 
as defined above will be used hereafter. Thus, if 
induced emf is expressed in volts and 4> in maxwells, 
d4> 

e (volts) = —n,— X 10“S (4) 


The value of H in oersteds in the solenoid, when the 
current i is expressed in amperes, is 


4ti4i 



(5) 


1.2 HYSTERESIS, REMANENCE, COERCIVE 

FORCE 

In Figure 3 are shown the results of measurements 
made on a sample of hard-drawn unannealed nickel 
tubing. Starting with the sample in the unmag- 
netizcd state, the values of B for increasing values of 
// are shown by the solid cim'e. The measured 
values of B, when 77 is decreased step liy step from 
its maximum value, are shown on the broken curve. 
For any given value of 77 the value of B is greater 
when the magnetizing field is decreasing than when 
it is increasing. The phenomenon is known as 
hysteresis. When the field is reduced to zero, the 
flux den.sity still has a value Br. The value of the 
flux density which remains in a magnetic material 
after the magnetizing field is removed is called the 
remanence. The magnitude of Br will depend upon 
the maximum value of B which was initially at¬ 
tained. The value of B at which an increment in 77 
produces no more than an equal increment in B is 
called the saturation value. Retentivity is the rema¬ 
nent flux density after a magnetizing field sufficient 
to produce saturation has been removed. 

If an alternating field is applied, the values of the 
flux density will describe a closed hysteresis loop, the 
upper half of which is shown in Figure 3. In such 
a process the material is said to be cyclically mag¬ 
netized and the hysteresis loop is symmetrical about 
the origin. The value He for which B is zero is called 
the coercive force. If the initial magnetization has 
been carried to saturation, then the coercive force is 
de.signated as the coercivity. 

In Figure 3 the solid curve is the “normal mag¬ 
netization” curve for the sample. Obviously the 
value of M as previously defined will depend upon 
the previous history of the samjile. Thus, for any 
value of 77, three different values of B are shown, 
and hence we have three different values of y. One 
of these, the static permeability, is considered to be 
the value of B 77 as given by the normal magnetiza¬ 
tion curve. In Figure 4, the values of y and k 
(siLSceptibility) for the sample of hard nickel shown 
in Figure 3 are plotted against 77. The magnetic 
properties of materials under the action of alter¬ 
nating fields will be discussed in Chapter 4. 

1.3 STATIC MAGNETOSTRICTION — 

HISTORICAL 

As already noted, the magnetization of ferromag¬ 
netic material sets up internal stresses and resultant 


CONFIDENTIAL 














4 


INTRODUCTION 


strains. Conversely, externally applied stresses gen¬ 
erally produce changes in the magnetic state. In 
1847, Joule''* reported “The Effects of Magnetism 
upon the Dimensions of Iron and Steel Bars.” In 


the strain in an annealed .sample of nickel is plotted 
against the applied magnetic field. In Figure 6 the 
linear relation between the logarithm of the strain 
and the log {B - H)- is shown. 



-He-H H IN OERSTEDS 

Figure 3. Remanence and coercive force of hard-drawn nickel. 


his experiments the test specimen, a bar of iron or 
steel fixed at one end, was mounted in a magnetizing 
solenoid. The change in length under constant stress 
was amplified by a system of levers and measured 
with a micrometer microscope. What he called the 
“magnetic intensity” was measured by balancing 
the pull exerted by the induced magnetic pole on 
one end of a suspended magnet by weights applied 
to the opposite end. As the results of numerous e.x- 



Figure 4. Permeability and susceptibility of hard- 
drawn nickel. 


bar is proportional to the square of the magnetic 
intensity and that the elongation is greater in an 
annealed than in an unannealed bar. In Figure 5 


In 1868, E. Villarireported the reverse magneto- 
strictive effect, namely, that varying the stress in 
a magnetized body will jtroduce changes in the 
induced magnetization or a change in the su.scepti- 
bility. In his experimental apparatus, the magneto- 
strictive sample was mounted along the axis of a 
.solenoid. A secondary winding around the sample 
was connected to a ballistic galvanometer. The 
galvanometer throw produced by longitudinally 
stre.ssing the magnetized bar at a constant value of 
H gave a mea.sure of the change in the induced mag¬ 
netization. By using bars of iron and steel he 
arrived at the conclusion that the change of mag¬ 
netization resulting from a constant stress increa.ses 
with the magnetizing field up to a certain value of 
the field. Beyond this value, the change in mag¬ 
netization for a given incremental stress decrea.ses 
with increasing field. In Figure 7 the change in 
magnetization of nickel is plotted for different values 
of the magnetizing field against the tension which 
produces it. 

Later studies made on ferromagnetic materials 
of the two magnetostrictive effects (the change in 
volume with magnetization — the Joule effect — 
and the change of susceptibility under mechanical 


COXFIDEXTIAL 














































































MAGNETOSTRICTIVE CONSTANT AM) YOUNCi'S MODULUS 


stress) have confirmed the fundamental discoveries 
of Joule and Villari. They have shown, however, 
that the relations involved are far from sim]de anti 
differ widely from material to material and with heat 
treatment and history for the same material." 

1.4 HYSTERESIS AND MAGNETO¬ 
STRICTION 

As in the case of the induced magnetization, the 
magnetostrictive effect does not follow the same 
course for a rising as for a falling magnetizing field. 


usually designed to operate at the resonant frequencj' 
of \’ibrating .systems in which the mechanical re.so- 
nance is comparatively high, thus enhancing the 
response at the driving frecpiency relative to the 
harmonic components of the distorted vibration. 

The data for Figure 8 were obtained from static 
measurements and show a much greater range in 
the value // than can be attained in actual practice 
with a-c fields. The somewhat complicated prob¬ 
lem of the relation between electric excitation and 
acoustic resi)onse will be considered in detail in later 
chapters. 



H IN OERSTEDS 

Figure 5. Magneto.strictive strain a.s a function of field for annealed nickel. 


This is .shown in Figure 8 for a .sam]de of annealed 
nickel wire.'^* Note the low value of dl/l when the 
field is reduced to zero, corresponding to the mag¬ 
netostriction under remanent magnetization; also 
note the similarity in shape to the shape of the mag¬ 
netization curve. However, since the magneto- 
strictive contraction is not dependent upon the 
direction of the applied field, the curve does not fall 
below the horizontal axis for negative fields as does 
the magnetization curve. Obviously the response 
frequency of a magnetostrictively driven de^’ice with¬ 
out biasing polarization will be double the tlriving 
frequency. 

Further, the nonlinearitj' between the exciting field 
and the strain indicates that distortion is to be ex¬ 
pected in magnetostrictive transducers. This effect 
is mitigated by the fact that such transducers are 


“ I'\)r an account of this work with reference to original 
papers, see reference.s 10, 2.5, and 27. For a resume of the 
data on iron and nickel alloys, see reference 31. 


1.5 MAGNETOSTRICTIVE CONSTANT 
AND YOUNG'S MODULUS 

Joule concluded from his experiments that the 
change in length of a rod in a magnetic field is pro¬ 
portional to the square of the induced magnetization. 
Later work has shown that for moderate flux densi¬ 
ties in most ferromagnetic materials the strain is 
approximately proportional to the square of the flux 
density. We may therefore write 

s = cB'-, 

where c is simjily a proportionality factor, which is 
positive for a material that ex])ands with increa.sing 
magnetization and negative for one that contracts. 
Permalloy expands when magnetized and c is posi¬ 
tive. In the case of nickel the reverse is true and c 
is negative. Following the usual convention, tension 
and expan.sion are treated as positive stress and 
strain resjiectively, whereas pressure and contraction 
are considered negative. 


CONFIDENTIAL 































6 


INTRODUCTION 


If the flux density in a sample of magnetostrietix’e 
material is changed from Bo to Bo + dB without 
change of stress, then the strain changes by an 
amount 


or 


5s = :—{cB-)5B = 2cBo8B, 
oB 


dB. 


= 2cBo 


-ip 


(fl) 


Conversely, if the length of the magnetostrictive 
sample is kept constant (6s = 0) while the flux 
density changes from Bo to Bo + 8B, the stress 
changes b}" an incremental amount, 

^■^^(ronstaiit s) — — X5B. (7) 


The magnetostriction constant X is defined by the 
equation 


X = - 




Figure 6. LoKaiitlim of strain vs log (B-II) for 
annealed nickel. 


The negati\-e sign here may perhaps be (luestioned, 
but it follows our convention of signs for stresses 
and strains. If, for example, in a given material 
under constant stress, an increase in B produces an 
increase in length (positive strain), then in order to 
keep the length (strain) constant when B increases, 
a pressure (negative) stre.ss must be aitplied. Nickel 
contracts with increasing B, or [ds dB]/> is negative. 
Hence a tension (positive stress) must be applied to 
keep the length constant under increasing mag¬ 
netization, so that X for nickel is intrinsically nega¬ 
tive. 

If a magnetostrictive rod is simultaneously sub¬ 
jected to a change of magnetization bB and an in¬ 


cremental strain 5.s, both acting along its length, 
then bP, the total stress, is given by the equation 


bP = Ebs -|- 


"dP 


bB = Ebs 


XbB, 


(8) 


where E = \ bP/bs |/; is the Young’s modulus at 
constant flux density. 

It will be shown in a later chapter that a change 
bB in B in a magnetostrictive material arises from 
two causes — a change bH in the external mag¬ 
netizing field and a second change produced by the 



Figure 7. Incremental magnetization as function 
of aj)i)lied stress in nickel. 


incremental strain 5s. The total increment in B 
then is given by the relation 

bB = iJir{bfl -iwXbs), (9) 

where nr is the reversible permeability (defined in the 
next section) of the material at the itarticular \'alue 
of Bo from which the change occurs. From equa¬ 
tions (8) and (9), 

bP = Ebs — XjiribH -)- 47rX5s) 

= —Xyrbll {E - iirX-fjir)bs. 

Suppose that B equals Bo, H is held constant 
{bH = 0) and an incremental stress bP is aitplied. 
Then from eciuation (10), 

= {E - iTrXVr) = E'. (11) 



C'ONFIDENTIAL 































































KEVERSIBLE PERMEABILITY 


Here E' is the effective Young’s modulus of the 
magnetostrictive material at a given value of H and 
a corresponding ^•alue of B, and it is this modidus 
that determines the resonant freciuency of a mag- 
netostrictiv'e transducer. E' may he written in the 
form 

= E{\ - k% (12) 

where k = 



APPLIED FIELD Hq 

Figure S. Hysteresis in magnetostrictive strain. 


and is called the coefficient of electromechanical cou¬ 
pling. It is a measure of the degree of coujiling that 
can be obtained lietween the electrical and mechan¬ 
ical sides of a transducer. Both the.efficiencj' and the 
breadth of the frequenc,v resiionse will be shown to 
depend upon the value of k. Since both Ur and X 
are functions of B, it is obvious that the maximum 
value of k corresponds to the value of B, for which 
XVr is a maximum. Hence the magnetostricti\'e 
elements of a transducer should be polarized to gi\’e 
this value of B if the tran.sducer is to operate at 
maximum efficiency. 

Table 2 shows the effect of lamination thickness 
and polarizing flux density on magnetostrictive 
quantities. Table 3 gives the several jiroperties of 
magnetostrictive materials. 


de.scribe a minor hy.stere.sis loop. If// = //o ± 5H '2 
(Figui-e 9), then the total swing in II will be 8II, from 
which will result a cyclical change in the flux density. 
The reversible permeability Mr is defined as the 
limiting value of dB 8II as 8II approaches zero. If 

Table 2. Effect of thickness and polarizing flux den¬ 
sity on magnetostrictive cpiantities.* 


Thickness 


Material 

(inch) 

Bo 

X X 10-^ 

Max eff 

A-nickel 

0.002 

4,000 

1.25 

0.78 

(1 hr at 1000 C 

0.002 

5,000 

1.99 

0.83 

in Hj) 

0.002 

5,500 

2.10 

0.83 


0.001 

12,000 

0.39 

0.82 


0.002 

12,000 

0.32 

0.70 


0.002 

13,000 

0.48 

0.75 

45-Permalloy 

0.002 

14,000 

0.62 

0.80 


0.004 

12,000 

0.35 

0.60 


O.OOf) 

12,000 

0.27 

0.25 


0.014 

12,000 

0.36 

0.15 



0.002 

16,300Rt 

1.07 

0.85-0.93 

2V-Permendur 
(annealed 1 hr 
at 5.50C in H-') 

0.002 

0.004 

0.006 

to 

19,400Rt 

14,300Rt 

18,360R 

to 

1.25 

0.92 

1.04 

0.82 

0.77 


0.012 

10,200R 

0.69 

0.17 


* Maynetic Materials for Magnetostriction Microphones and Projectors^ 
Williams. Nesbitt, and Goertz, Hell Telephone Laboratories. Inc.. March 22, 
1944. 

t Rem.ancnt flux density. 


B 



Figure 9. Reversilile |iermeahility. 


1.6 REVERSIBLE PERMEABILITY 

Reference has been made in the foregoing treat¬ 
ment to “reversible permeability.” If II varies peri¬ 
odically about a constant biasing field IE, then B will 


in static measui-ements bll is from 10 to 20 per cent 
of IE, the measured value pj will approach very 
nearly the true reversilile permeability. In Figure 10 
are shown measured values of pj plotted against I = 
{B — II) for two samples of commercial nickel 


CONFIDENTIAL 




















8 


INTRODUCTION 


annealed in air at 1000 C. Here is an illustration of 
what seems to be generally true, that is, for mag¬ 
netically soft materials, the reversible permeabilities 



INTENSITY OF MAGNETIZATION (I) 

Figure 10. Reversible permeability of nickel as a 
function of (B - H). 


SO plotted fall on a straight line. IMore accurate 
measurements of Mr can be made by alternating- 
current methods, which will be considered in detail 


in Chapter 4. Hereafter, unless otherwise stated, it 
will be the reversible permeability with which we 
are concerned here, designated simply as m or n' (see 
Chapter 4) without the subscript. 


1.7 MAGNITUDE OF MAGNETO- 
STRICTIVE FORCES 


Some simjde calculations based on the data pre¬ 
sented above will serve to give an idea of the order 
of magnitude of magnetostrictive forces. 

For most design purposes the following numerical 
values for nickel are adequate: 

Young’s modulus E = 2.10 X 10‘- djmes per sq cm. 
Density p„ = 8.9 gm per cu cm. 

\Ylocity of sound c„ = 4.9 X 10° cm per sec. 

As a numerical illustration, consider a nickel rod 
whose fundamental longitudinal resonance frequency 
fr is 20 kc. The length of the rod having this 
resonance frequency 


^ _ 4.9 X 10^ 
2fr~ 2X2 X 10^ 


12.3 cm. 


For a magnetizing field of 125 oersteds, we have 
from Figure 5 dl/l = — 25 X 10“'^, and the con¬ 
traction of the rod would be 25 X 10“® X 12.3 = 
3.1 X 10“^ cm. If by some mechanical restraint 
the length of the rod is kept constant, the re¬ 
sultant stress equals 25 X 10“'’ X 2.10 X 10’- = 
5.5 X 10' d 3 mes per sq cm = 800 11) j)er sci in. 


T,\ble 3. Properties of magnetostrictive materials.’* 


He = Coercive force (oersteds) 
n = Reversible permeability 
Bo = Polarizing flux density 


k = Coupling coef. = ' 

X = Magnetostrictive constant 
Pe = Resistivity ohms-cm. 


Maximum efficiency for an assumed (^ = 4: 
All tests made on samples 0.002" thick. 


Material 

Heat treatment 

P. X io« 

He 


Bo 

X X 10-' 

k 

Max eff 


Inannealed 

8.0 

19. 

13 

3,200Rt 

1.02 

0.09 

0.61 


600 C 

8.0 

14.3 

30 

3,640Rt 

1.10 

0.15 

0.79 

.\-iiickel 

1000 C 

8.0 

0.76 

166 

2,128Rt 

0.44 

0.14 

0.39 


1000 C in H, 

8.0 


78 

4,000 

1.25 

0.27 

0.78 


1000 C in H. 

8.0 


41 

5,000 

1.99 

0.32 

0.83 


Unannealed 

45 

7.60 

53 

8,600Rt 

0.31 

0.054 

0.64 

4.5-Permalloy 

1000 C in H. 

45 

0.26 

1,768 

5,840Rt 

0.05 

0.008 

0.045 


1000 C in H, 

45 


372 

12,000 

0.32 

0.16 

0.70 


1000 C 

25 

1.90 

42 

9,920Rt 

0.40 

0.06 

0.76 


800 C 

25 


91 

20,000 

1.37 

0.32 

0.90 

2V-Permendur 

650 C 

25 

9.1 

126 

13,950Rt 

0.85 

0.21 

0.92 


600 C 

25 

18.4 

59 

17,500Rt 

1.23 

0.24 

0.92 


* Magnetic Materials for Magnetostriction Microphones and Projectors, Williams, Nesbitt, and Goertz, Bell Telephone Laboratories. Inc., 
March 22. 1944. 

t Remanent flux densitj*. 


CONFIDENTIAL 







































>IAGNETOSTRICTIVE VIBRATIONS 


9 


The maximum alternating stress that can usefully 
he produced by the magnetostriction of nickel has 
been calculated to be between 2.5 X 10^ and 10 X 10^ 
dynes per sq cm. For the 20-kc half-wave rod this 
would correspond to a contraction of 1.47 X 10“^ cm. 
These values are for the stress within the nickel in 
the region of maximum strain — that is, at a motion 
node. The pressure that could be exerted upon 
water in any actual case would depend on a number 
of factors, for example, the sharpness of the mechan¬ 
ical re.sonance of the vibrator and the ratio of the 
cross section of the surface in contact with the water 
to the cross section in the region of maximum strain 



in the nickel. In some experiments on the maximum 
obtainable output of laminated nickel stacks made 
at the Harvard Underwater Sound Laboratory 
[HUSL], acoustic pressures as great as 8 X 10'’ 
dynes per sq cm (approximately eight atmospheres) 
were produced in an oil-filled pressure chamber by a 
stack of nickel laminations driven by magnetostric¬ 
tion. This is roughly 12,000 times the pressure in 
an atmospheric sound wave that is at the threshold 
of pain for the human ear. There is an obvious ad¬ 
vantage in applying magnetostrictive vibrations of 
small amplitude and large force to the generation of 
acoustic waves in a highly incompres.sible medium 
like water. 


1.8 MAGNETOSTRICTIVE VIBRATIONS 

It is difficult to assign a date or allocate the credit 
for the first application of magnetostriction to the 
generation of acoustic waves in water, but it can be 
said that recognition of the possibility of such an 
application stems from the researches of G. W. 
Pierce and co-workers at Harvard in the period 
beginning about 1925. The original notes of Pierce’s 
experiments, which he placed at the disposal of 
the HUSL group, proved of invaluable help in the 
initial stages of the work in this field at Harvard. 
In his handbook on underwater sound technique 



Figure 12. Early example of radially vibrating 
cylinder. 


published in 1922, Aigner makes no mention of 
underwater devices operating on this principle. The 
small amplitude attainable makes possible only 
small amounts of radiated power at audible fre¬ 
quencies. Since the radiated power is proportional 
to the square of the product of the amplitude and 
frequency, it is generally necessary to go to super¬ 
sonic frequencies to realize acoustic powers of useful 
magnitude. Prior to the development of vacuum- 
tube oscillators and amplifiers, electric oscillations 
in the supersonic range were not easily obtained. 
Moreover, the earlier use of piezo-electric crystals 
for the production of high-frequency mechanical 
vibration pretty well pre-empted the field. 


CONFIDENTIAL 












































































































































































































































10 


INTKODUCTION 



Figure 13. .\n underwater sound magnetostrictive 

device to be operated at a frequency of about 18 kc. 

It was toroidally wound on a nickel tube about 4 in. in 
diameter and oil-filled with an outer jacket of rubber. 

B. Stacks of magnetostrictive laminations toroidally 
wound for supersonic applications. 

clamped at the midpoint and excited by mean.s 
of an alternating current superimposed on a direct 
polarizing current. He suggests a means of gen¬ 
erating sound waves in water bj' attaching a mag¬ 
netostrictive rod to the steel plates on the opposite 


In a patent application filed January 3, 1927, 
Pierce-' -''di.sclosed a magneto.strictive oscillator con- 
.sisting esisentially of a magnetostrictive tube or rod 


Figure 14. Magnetostrictive unit designed for alti- 
drift measurements on the dirigible I'SS Akron. It 
was designed to operate at about 8 kc. A similar unit 
about one foot in diameter surrounded by a metal 
cone was also tried for underwater echo ranging 
(X933-34). 


CONFIDENTIAL 
























TYPES OF MAGNETOSTRICriVE TRANSDUCERS 


11 


sides of a ship’s hull and exciting the rod with tuned 
alternating current in a coil surrounding the rod. 

One of the earliest experimental studies of mag- 
netostrictive vibrations was reported in 1928 by 
K. C. Black,working with Professor Pierce. The.se 
studies were made on samjjles clamped at their mid¬ 
point within a magnetizing solenoid and free to 
vibrate longitudinally as half-wave oscillators, using 


electric energy or the reverse. The most efficient 
types of magnetostrictive transducers are those 
operating at or near a resonant frecjuency of the 
magnetostrictive driving member. Two general 
types have been developed: (1) those employing 
the longitudinal vibrations of.rods, tubes, or laminae, 
and (2) those emjdoying the radial vibrations of 
tubes or rings. For a transfer of power from the 



Figure 1.5. Air horns built at XRL in May 1929. The individual tubes, driven longitudinally, were anchored to the 
vertical members of the vibrating system. The .shape of the vibrating area was such as to produce mechanical ampli¬ 
fication of the magnetostrictive displacement. 


the impedance methods developed by Kennelly and 
Pierce 22 for the study of telephone receivers. 
Samples of Invar, stainless steel, and nickel were 
studied. Under applied alternating fields at reso¬ 
nance, vibrational amplitudes were produced .several 
hundred times as great as the static displacement by 
a d-c field of equal strength. The motional imped¬ 
ance in annealed nickel was found to reach a 
maximum with a polarizing field of about 30 oersteds. 

The resistive component of the motional imped¬ 
ance at resonance and the lag between the magnetic 
flux and applied current were greater in rods than in 
tidies. The flux change due to the vibration was 
found to be greatest at the motion node. All these 
findings are of importance in the design of trans¬ 
ducers for underwater signaling. 

1.9 TYPES OF MAGNETOSTRICTIVE 
TRANSDUCERS 

For the purpose of this volume, a transducer maj^ 
be defined as a device for transforming acoustic to 


driving element into the medium, it is es.sential that 
the medium present the proper acoustic resistance 
to the motion of the driver. One of the means 
employed to this end is the tubc-and-plate, illustrated 
in one of its earliest forms in Figure 11.-™ Here the 
driving elements are magnetostrictive tubes whose 
length is approximately a quarter of the wave 
length, in the metal, of the sound to be radiated. 
These are .set in massive blocks tuned to the same- 
frequency and are driven in phase by the alternating 
currents in the coils. Polarizing fields for the- 
magnetostrictive tubes are supplied either by a 
d-c component of the current or by permanent 
magnets. The alternating pressure exerted on the- 
jfiate by the driving elements is ti-ansmitted. over- 
the entire area of the oppo.site face. A variant of the- 
tube-and-plate is the tuhc-and-cone. Here- the- force 
of the driving element is applied at the- apex, of the 
cone, which operates in a manner somewhat analo¬ 
gous to the horn of a loud-speaker aa an impedance 
transforming device. 

The radially vibrating tube is ilhrstrated. in. one of. 


CONFIDENTIAL 



12 


INTRODUCTION 


its earlier forms iii Figure 12.-^ Here the energizing 
eoil is wound toroidally and the polarizing and 
alternating flux is cireumferential. The lowest radial 
resonant vibration occurs at a frequene.y for which 
the wave length in the metal is t'qual to the circum¬ 
ference of the tube. A variant of the tube type is 
the consolidated stack of ring laminations. Internal 
windings on diametral cores of highly permeable 



Fiovre 16. Production model of the XQC projectors. 

material and armature-type windings on nonmetallic 
core forms have been used. Since the radially 
vibrating tube transducers afford a closed magnetic 
circuit, they may for certain uses Ite operated on 
magnetic remanence. Tubes of unannealed and of 
half-hard nickel with remanent polarization have 
found extensive use in underwater listening devices. 
Permanent-magnet ijolarization of annealed-nickel 
tubes has been effected by means of Alnico magnets 
placed on a diameter or inserted in the circumference. 


The preceding illustrations, Figures 13 to 16, are 
j)hotographs of a number of early experimental 
magnetostrictive transducers made at the Anacostia 
Naval Research Laboratory.'’ 

Ring stacks of half-annealed 2\'-Permendur (iron- 
cobalt-vanadium alloy) have been found to be 
operable at high levels and with relatively high 
efficiency on remanence. 

Figure 17 shows a prototype of laminations which 
have received considerable attention in the develop¬ 
ment of laminated stack transducers. The lamination 


o 



Figure 17. Lamination of asymmetrical stack trans¬ 
ducer. 


is a strip of metal whose width is approximately one- 
half the wave length in the metal of the frequency 
to be radiated. Winding slots are cut in one half of 
the lamination. The legs between windows, around 
which are the coils for alternating and direct current. 

These photographs were supplied through the courtesy 
of Dr. Harvey C. Hayes, Naval Research Laboratory, 
Anacostia, Maryland. They ilkustrate some of the early 
work on magnetostrictive acoustic devices done at NRL. 
The covering letter from Dr. E. D. Klein, Associate Superin¬ 
tendent of the Sound Division, states: 

“ These and various other devices which dealt with magneto¬ 
strictive elements were worked on progressively from 1927 to 
1935. Only a limited few were tested in service for echo¬ 
ranging purposes, due to their being replaced by crystals in 
our development program.” 


CONFIDENTIAL 







































ClIAKACTERISTICS OF TRANSDUCERS 


constitute the driving elements. The thickness of 
the legs and of the arches of the window is designed 
to secure the proper impedance match with the 
water. The HP type of laminations used in the 
magnetostrictive scanning .sonar transducers is a 
developed form.* All the various transducers de¬ 
signed for special uses and described hereafter will 
be seen to be modifications of one of the general 
types listed above. 


1.10 CHARACTERISTICS OF SOUND \\ AVES 

Any variation in the physical properties of a 
medium that is propagated through the medium is 
called a leave. A sound wave in water consists of a 
propagated change in particle di.splacement, particle 
\'elocity, and pre.ssure. The velocity of jjropagation 
c is given by the familiar equation c = V E 'p, where 
E is the volume elasticity and p the density of the 
medium. The velocity of sound in .sea water is 
api^roximately 1,500 meters pei- second. 

The intensity of sound in a ])lane or spherical wave 
is the rate at which vibrational energy is tran.s- 
mitted across a unit area of cro.ss section normal to 
the direction of prolongation. If the particle di.s¬ 
placement is a sinusoidal function of time, then the 
intensity of sound E at any point on the wave is 
gi\-en by the equations 

h = 2ir-'-pcAT = (13) 

2pc 

where A, U, and P are the amplitudes of the di.s¬ 
placement, the velocity, and the pre.ssure respec- 
ti\’ely. Denoting the root-mean-square (rms) values 
of \’elocity by u and pressure by p, 

p* 

Is = pcu-= — (ergs Asec/cm-) (14) 

pc 

= — X 10“^ watts/cmA 
pc 

In a free field, p is the rms force in dynes per square 
centimeter exerted on a thin lamina of the medium, 
and u is the rms particle velocity in centimeters per 
second. The acoustic resistance of the medium de¬ 
fined as p/ti equals pc. 


1.11 DECIBEL NOTATION 

The decibel scale is used to expre.ss the ratio of 
amounts of power and energy, as well as other 


1.1 


cpiantities proportional thereto. It is a logarithmic 
scale in which the numerical values corresponding 
to .successive, equally spaced graduations on the 
scale bear a fixed ratio one to another. One decibel 
difference on the scale corresponds to a ratio whose 
logarithm is O.I (1.259:1). The decibel level re¬ 
ferred to unity for any quantity which varies directly 
as a i)ower or an energy is numerically 10 times the 
logarithm of the numeric of the (piantity. Thus: 


Power level 


1 watt 
10 watts 
20 “ 
40 “ 

100 “ 


= 10 log 1 
= 10 log 10 
= 10 log 20 
= 10 log 40 
= 10 log 100 


0 dh 
10 “ 
13 “ 
10 “ 
20 “ 


ref. 1 watt 


Since the jiower in an electric circuit of fixed 
impedance varies as the square of the apijlied voltage 
or as the scpiare of the current and since the inten.sity 
of .sound is proportional to the square of the acoustic 
pre.ssure, the decibel level of these quantities is 20 
times the logarithm of the numeric of the quantity 
in each case: 


Voltage 

level 


f 1 

volt 

= 20 

log 

1 

= 0 dh ref. 

1 volt 

! 10 

volts 

= 20 

log 

10 

= 20 “ “ 

u a 

' 20 

U 

= 20 

log 

20 

= 2(3 “ “ 

u » 

40 


= 20 

log 

40 

= 32 “ “ 

M a 

[lOO 

u 

= 20 

log 

100 

= 40 “ “ 

a a 


Similarly, the pressure level of acoustic pressure 
referrt'd to 1 dyne per square centimeter is 20 times 
the logarithm of the pressure. 


1.12 CHARACTERISTICS OF TRANS¬ 
DUCERS 

iMost magnetostrictive transducers are reversible. 
They may be used to produce an electric signal in 
response to an alternating acoustic pressure. When 
so used they will be spoken of as hydrophones. When 
used in the reverse manner, to radiate acoustic en¬ 
ergy under electric driving, they will be referred to 
as projectors, or sometimes simply as transmitters. 

The performance of a transducer, either as a h}'- 
drophone or as a projector, may be described in a 
variety of ways. Imagine, for example, the existence 
of a uniform sound field consisting of plane waves 
traveling in a certain direction in open water. Let 
the rms pre.s.sure due to the waves be p. This 
prassure is a.ssumed to be measurable by means 
of a standard so small that its presence does not 
appreciably distort the field. Now suppose that an 
unknown transducer is inserted into the sound field. 


CONFIDENTIAL 




It 


INTRODUCTION 


so oriented as to oldaiii a maximum electric output. 
Let E l)e the rms voltage developed at the output 
terminals of the transducer when no current is 
drawn from it. The ratio E 'p is now defined as 
the open-circuit (voltage) sensitivity. Notice that 
p is the rms pressure in the sound field before the 
introduction of the hydrophone. The sound field 
will be more or less distorted by the hydrophone, 
but the pressure calculated from a known sensitivity 
and open-circuit voltage will, by definition, still be 
the correct value for the undisturbed field. 

Other definitions of sensitivity are sometimes use¬ 
ful. Suppose, for example, that the hydrophone 
is short-circuited instead of open-circuited, other 
conditions being the same as specified above. Let 
the rms current which flows be I. Then the short- 
circuit (current) sensitivity is defined as the ratio 
7,/p. The open-circuit voltage E and the short-cir¬ 
cuit current I are related by Ohm’s law — E = l\z\ 
where Z is the electric impedance of the transducer 
(in water). Thus the open-circuit (voltage) sensi¬ 
tivity is just \Z\ times the short-circuit (current) 
sensitivity. Under other conditions of measurement, 
it may be convenient to define additional .sensi¬ 
tivities which will be rather simply related to the 
two already used. In this report, the first definition 
will be most frequently used and the term “sensi¬ 
tivity,” unless otherwise qualified, will refer to the 
open-circuit (voltage) sensitivity. 

In practical applications the sensitivity is usually 
expressed in decibels relative to a sensitivity of one 
volt per dyne per square centimeter. Sometimes a 
distinction is made between sensitivity expressed in 
\-olts per dyne per square centimeter and 20 times 
the logarithm of this quantity, which is then called 
the (open-circuit) recei^’ing response. However, the 
terms “sensitivity” and “receiving response” .shall 
be considered interchangeable and shall be ex])ressed 
either in volts per dyne per square centimeter or in 
decibels relative to one volt per dyne per scpiare 
centimeter. 

The threshold of a hydrophone is expressed in terms 
of the pres.sure level in a uniform plane-wave free 
sound field parallel to the acoustic axis of the device, 
in decibels vs reference pre.ssure (1.0 dyne per sq 
cm) which produces a signal voltage equal to the 
inherent noise voltage. This noise voltage is taken 
in a band width of one cycle when the device is in a 
matched tuned circuit. For magnetostrictive trans¬ 
ducers, the inherent noise is the thermal noise, and 
it can be shown that the threshold, as defined above. 


of a transducer of this type whose resistance is R is 
given by the efjuation 

Thre.shold = 10 log 7? — 194.9 — sen.sitivity.'’ (15) 
(Sensitivity here is expre.ssed in decibels.) 

1.1.3 RESPONSES OF PROJECTORS 

To ob.serve the performance of a transducer in 
transmitting (as a projector), suppose that it is 
placed in open water with no near-by obstructions 
which could reflect sound energy. When electric 
power is .supplied to the transducer, acoustic power is 
radiated. The direction in which the intensity is 
greatest is the .same as the direction in which the sen¬ 
sitivity is greatest and will be called the acoustic axis. 
Except at points very close to the transducer, the 
pressure falls off as the inverse first power of the 
distance. Let pi be the rms pressure one meter from 
the transducer, assuming that the pressure in this 
vicinity is already falling off inversely with the 
distance. Otherwise is defined as the pre.ssure on 
the axis at some great distance multiplied by the 
ratio of this distance to one meter. 

Now, the transmitting performance of the trans¬ 
ducer can be specified by giving the ratio of pi to 
some appropriate ciuantity connected with the 
electric input to the tran.sducer. The current-trans¬ 
mitting response will be defined as the ratio of pi to 
the rms current delivered to the tran.sducer. Like¬ 
wise, the voltage-transmitting response is the ratio of 
pi to the rms voltage across the tran.sducer. As in 
receiving, other responses may be defined in terms 
convenient for certain instances. 

The various responses in transmission and re¬ 
ception are connected by relations which will be 
given shortly. 

The efficiency of a projector is defined as the ratio 
of the total acoustic power delivered by the projector 
to the electric jjower input into the projector. Since 
this is the ratio of two jjowers, it may naturally be 
expre.ssed in decibels: 

Pa 

Efficiency (decibels) = 10 log—’ (10) 

where Pa and P^ are the acoustic power output and 
the electric power input respectively. Efficiency is 
expressed in decibels rather than as a simple ratio or 
percentage because .sound-measuring equipment is 
generally calibrated in decibels, hence measured 
\'alues are averaged in logarithmic rather than in 


CONFIDENTIAL 



RECIPROCITY 


13 


linear units, and probable errors should properly be 
expressed in decibels. 

The acoustic power output is found by integrating 
the energy-flux density (= p-/pc) over a sphere of 
radius r. 


Let p = density of the medium (gm per cu cm), 
c = velocity of sound (cm per sec), 
p = rms acoustic pressure (dynes per sq cm). 


Pa = — ( fp’da = - p'‘D (ergs/.sec) 

pc J J pc 


Sphere 


~p''l) X 10-" (watts), 
pc 


(17) 


p' is the value of the acoustic j^ressure measured at 
the principal maximum of the radiation pattern, and 
D is the directivity ratio, defined as the ratio of the 
average value of pi- over the entire sphere to its 
value at the principal maximum. The precise evalu¬ 
ation of the value of D is in general a matter of some 
difficulty, since it involves the integration of p- over 
the entire sphere. The experimental data required 
are obtained by placing a measuring hydrophone, 
connected to recording equipment, in the water at a 
distance from the projector — great in comparison 
with projector dimensions. If the projector is 
rotated about an axis, the relative pressures in all 
directions in a plane perpendicular to that axis are 
recorded. Depending upon the geometry of the 
radiating face, patterns in one or more planes will be 
reejuired to give the needed information for evalu¬ 
ating D. 

The electric power input is obtained directly from 
the measured value of the input voltage Ei and the 
impedance Zi = Ri jXi of the tran.'^ducer. 


Pe = 


Ei 1 ^/?.- 

I 1“ 


(18) 


From equations (17) and (18), 

Pa 4Tf~ ■ p"D • I Z 10-’ 
^ ~ Pe^ pc ■ 1P\ Ei 1 '^ 


(19) 


For sea water, pc = 1.55 X 10^ With the numerical 
values inserted and r exjiressed in meters. 


Eff (decibels) = 20(log r -|- logp' — logFi -|- logZ,) 
-h 10(log D - log Rd - 70.9. (20) 

If the power input P« can be directly measured, 
then equation (20) may be written: 

Eff (decibels) = 20(log r -f log p') 

-f- 10(log D — log Pe) — 70.9. 


1.11 RECIPROCITY 

Most of the transducers to be considered in this 
report are linear, passive, reversible systems and 
satisfy a reciprocity theorem. The reciprocity 
theorem states that the performance of the trans¬ 
ducer, in a sense to be specified more completely 
below, is the same in transmitting as in receiving. 
Whether or not any particular system is reciprocal 
can be decided only by exjjeriment. It may, of 
course, be proved explicitly that an ideal transducer, 
employing a particular type of electromechanical 
coupling, is reciprocal by making use of the basic 
laws governing the coupling. Thus, for example, the 
experimental laws of magnetostriction will be used 
in Chapter 3 to show that magnetostrictive trans¬ 
ducers satisfying the conditions of linearity, etc., are 
also reciprocal. On the other hand, it is quite 
possible to construct mongrel transducers which sat¬ 
isfy all the other conditions but are still not re¬ 
ciprocal. 

Later in this book reciprocity in electromechanical 
systems will be discussed by regarding them as 
analogous to purely electric systems. It will be 
understood that no proof of reciprocity “ will be 
undertaken but that the purpose of the discussion 
will be to establish the meaning of reciprocity and 
to show its connection with the same term as applied 
to electric systems. The usual statement of reci¬ 
procity applicable to an electric circuit composed 
of invariable reversible elements is as follows: 

“If any electromotive force E is applied in any 
branch and the current I is measured in any other 
branch, then their ratio (frequently called the trans¬ 
fer impedance) E/I is equal in magnitude and phase 
to the ratio obtained if the positions of E and I 
are interchanged.” 

In Chapter 2, a slightly different form will be used, 
equating mutual impedances instead of transfer 
impedances. For the purpose at hand, the reci¬ 
procity theorem for a circuit is stated in a less 
common form: First, let an electromotive force Ea 
be applied in any branch a and the open-circuit volt¬ 
age Eh be measured at a pair of terminals b formed 
by breaking any other branch. Second, let a gen¬ 
erator be connected at b which produces a current 
Ih in this branch and let la be the resulting current 
in branch a. Then the ratios Ea/E^ and /(,//„ are 
equal in both phase and magnitude. An analogous 
statement of reciprocity in an electromechanical sys¬ 
tem can be obtained immediately by replacing the 


CONFIDENTIAL 





16 


INTROnUCTION 


voltage and current at the terminals b by a force and 
velocity respectively, or other suitable ciuantities in 
the mechanical system. C'onsider the arrangement 
in Figure 18A, which shows a voltage E' applied to 
a transducer and a pressure p' produced at a point 0 
in the sound field. The ratio E'/p' is analogous to 
the ratio EJE,, above. Here, instead of force and 
velocity, pressure and \’olume velocity will l)e con¬ 
sidered as being analogous to voltage and current 





■ 

o 


—u 



A TRANSDUCER AS TRANSMITTER 


is used with the same unit of power throughout. 
Cims multiplication in equation (21) yields an 
ecpiality between two cpiantities with the dimensions 
of power. One of these is electrical and the other 
mechanical. In practice, the mechanical unit of 
power is the erg ])er second while the electric unit is 
the watt equal to 10^ ergs i)er sec. Thus, for common 
usage, 

E' Q" 

- = + 4;: X l()-^ (21b) 

V i 

where E' and 7" are measured in volts and amperes 
and p' and Q" are measured in dynes per square 
centimeter and cubic centimeters i)cr second re¬ 
spectively. 



B TRANSDUCER AS RECEIVER 

Figure 18. Transducer in transmission and reception. 


respectivel.y. Pres.sure and volume velocity are con¬ 
jugate in the sense that their product repre.sents 
jiower. Figure 18B shows the transducer in re¬ 
ception. A small spherical sound source Q" is placed 
at the point where p' was previously measured. The 
source has a strength (rms volume velocity) Q" and 
it produces a current 7" in the transducer, which is 
now short-circuited. The ratio Q"/!'' is analogous to 
our pre\'ious 7(,/7„. Thus, by compari.son with the 
purely electric systems, the electromechanical system 
is said to be reciprocal if 


El = 91 

p' I"' 


( 21 ) 


Ideal electromechanical tran.sducers employing 
electrostatic or piezoelectric coupling do satisfy 
equation (21). On the other hand, if the coupling 
is electromagnetic or magnetostrictive, equation 
(21) holds in magnitude but the two sides are of 
opposite sign. Therefore, generalizing equation (21) 
the statement of reciprocity is taken to be 


E' Q" 


(21a) 


Generally, a transducer utilizing both types of cou¬ 
pling, one with positive and the other with negative 
sign, will not satisfy the reciprocity theorem. 

The statement of reciprocity for an electro¬ 
mechanical system, in the simple form of equation 
(21) is valid only if a consistent system of units 


].!."> VOLTAGE .SENSITIVITY AND 
EFFICIENCY 


To develop the relationship between ^•oltage sensi- 
ti\'ity and efficiency, the value of the acoustic 
pressure in a medium at a distance r cm from a 
sinijile source of strength Q mu.st be found. For the 
full mathematical treatment, the reader should con- 
.sult any of the standard texts on the theory of 
.sound. 

The rate at which energy is supplied to the sound 
field by a source of strength Q" located at the center 
of a sjihere of radius r is 


■iTrr'Ts 


irpcQ"^ 

X- 



( 22 ) 


where E i.s the intensity of sound as defined in 
equation (14), Q" is the strength of the source 
(= rms volume ^•elocity), and X is the wave length. 
Then 

p’’^ pcQ"^- 
* pc dr^X^ ’ 




(23) 


Eliminating Q from equations (21b) and (23), 


r 


10-^ = J 


E' 


(24a) 


The expression 2r/pf X 10“^ = .7 is the reciprocity 
parameter involving the frequency of the sound, the 
distance r in centimeters, and the density of the 
medium. If r be taken as 1 meter, p = 1.03, 


^ 2 X 10-’ 


1.94 X 10-" 

Tkc 


(24b) 


CONFIDENTIAL 




























ABSOI-UTE RECIBItOCITY CALIBRATION 


17 


Multiplying both sides of eciuation (24a) by 
the impedance of the transducer, 


v" 



Zi 



In equation (19), 

T''£f dTrr-Z) X 10“^ 

Kff = - X 

pcRi 

From ecjuation (24c) 


E' 


L P' h ^ u p-c-S- X 10'^ 

I r 4r-^M ’ 

irpcS'-D X 10’ 


Eff (decibels) = 20(log S — log X) 

+ 10(log D — log Ri) + 127. 


Zi 


(24c) 


(25) 


(25a) 


It will be obvious that agreement between the 
values of the efficiency as computed from equations 
(19) and (25) will depend upon strict linearity 
between the electric and acoustic powers over a wide 
range, since the actual magnitude of the electric 
power involved in sensitivity measurements is very 
small compared with that used in measuring trans¬ 
mitting response. 


1.16 RECEIVING AND TRANSMITTING 
RESPONSE 

If in equations (24a) and (24c) J = Ji, the 
value corresponding to a value for r of 1 meter, then 
ecpiation (24a) can be read: 

(Short-circuit [current] sensitivity) 

= Ji (voltage transmitting response). (26) 

Similarly, equation (24c) reads: 

(Open-circuit [voltage] sensitivity) 

= Ji(currcnt transmitting response). (27) 

Since the value of Ji varies inversely with fre- 
cpiency, a transducer having a sensitivity uniform 
with frequency over a certain range will have a rising 
current transmitting response proportional to fre- 
(jnency over this range. 

The change in sensitivity near resonance in a 
highly re.sonant transducer will be large compared 
with the change in frecpiency. Hence, over a small 
frecpiency range near resonance, change in J\ will be 
relatively small; current transmitting response will 
be nearly proportional to open-circuit sensitivity; 
and the frequency variation of the two will be 
nearly the same. 


1.17 ABSOLUTE RECIPROCITY 
CALIBRATION 

The measurement of the sensitivity or effi¬ 
ciency of an electromechanical transducer usually 
recpiires a calibrated standard whose sensitivity or 
transmitting response is known. A transducer 
known to satisfy the reciprocity theorem can be 
calil)rated without reference to arij^ other electro¬ 
mechanical standard. The principle underlying the 
method is most easily illustrated by visualizing two 
identical transducers which are both reciprocal. The 



Figure 19. Reciprocity calibration with two identical 
transducers. 


practical case in which there is only one reciprocal 
transducer is discu.ssed later in this chapter. In 
Figure 19, the transducers are arranged in water so 
that one is a projector and the other a hydrophone. 
The first is driven Iw a current I, producing a 
])ressure p at distance r meters (before the other 
transducer is introduced). The pressure is given b}" 

Til 

p = - 

r 

w’here the current transmitting response Tj is the 
l^ressure produced at one meter when the driving 
current is one ampere. When the second hydrophone 
is introduced, an open-circuit voltage E is generated, 
which is related to p and the open-circuit .sensi- 
tivitv »Sy bv 

E = Syp. 

Eliminating p from the two equations, 

SyTj = y • (28) 

Since both transducers are the same and reciprocal, 
the receiving and transmitting respon.ses are con¬ 
nected by 

= .hTj, 

where Ji is the reciprocity jDarameter for one meter, 
as defined previously. Solving for we find 



CONFIDENTIAL 


























1 « 


INTRODUCTION 


where J is the reciprocity parameter at distance r. 
Obviously the method as outlined is of no practical 
use because of the grave restriction to two identical 
transducers. 

This limitation may be removed as follows: Con¬ 
sider three transducers labeled T, B, and C. Trans¬ 
ducer A is to be used only as a transmitter, B only 
as a receiver, but C is to be used both in transmission 
and reception and is assumed reciprocal. All three 
transducers are assumed linear, but A and B need 
not be reciprocal. B and C will be compared as 
receivers (using T as a transmitter), then A and C 


C'onsidering experiment (1) by itself. 


(31) 


Sub.stituting equations (29) and (30) in (31) results 
in: 




E^Ezr 

~W’ 


which is essentially the same as equation (28) found 
previousl}" for two identical transducers. Treating 
it in the same way as equation (28), 


TRANSMITTER 


1_^ 


(1) 

A 

1_^ 


(2) 


1_^ 


13) 

C 




RECEIVER 



(meters) 


Figure 20. Reciprocity calibration u.sing three trans- 
ducens, one of which is reciprocal. 


comjjared as transmitters (using i? as a receiver), and 
finally an equation will be developed similar to (28) 
for A and B. Figure 20 .shows the experimental 
arrangement schematically. For the sake of .sim¬ 
plicity, suppose that the same current I is deli^’ered 
to the transmitters in each of the three experiments 
and that the spacing of the transmitting and recei\'- 
ing transducens is also the same. The (luantities Ei, 
El, and Ez are the open-circuit voltages pi-oduced in 
the three situations. Conditions ( 1 ) and (2) give an 
immediate comparison of the receiving performances 
of B and C. Thus 

EiSy^ 

(29) 

U-2 


Similarly ( 1 ) and (3) give a relation lietween the 
transmitting pei'formance of A and C: 

EiT^ 


Tj 


f.R 


Ez 


(30) 


= J,Tp = 


I / JEzEz _ 

I EJ~ 


(32) 


Eipiation (32) can be used in combination with 
equations (29) and (30) to ol:)tain and T^. 

Sometimes, in making a reciprocity caliliration, it 
will not be convenient to maintain the same current 
in the three experiments in Figure 20. If these 
currents are taken as 7i, 1 2 , and Iz respectively, and 
if the three distances are made Vy tz, and rz, it is 
found that equations (29), (30), and (32) become 


F T r 

a(B) r.iJ2)y>y 

^ ’ Ezhrz 

(29') 

rp(.i) EihnTP 

(30') 

TO) _ J ji(o _ \j•I'I\E2 Ez 
t Ei/ 2/3 ’ 

(32') 


where J' is the reciprocity parameter evaluated for 
the distance rzVz/ri. 

The simplest experimental jirocedure is as follows: 
The projector A (Figure 20) is located at a fixed 
])osition in the water and the transducers B and C 
are in turn located at a i^econd point at a distance r 
from .1. A fixed current I is maintained in A and 
the voltages generated in B and in C are measured. 
C is kept in position and A is replaced by B. The 
.same current I drives C and the voltage generated 
in B is measureil. In general, the measurement of 
the current I is the least accurate factor and there¬ 
fore ihe choice for the reversible unit of a tran.sducer 
of low impedance and fairly uniform response is 
desirable. Thin-walled tube-type magnetostrictive 
hydrophones meet these reciuirements to a fair degree 
and have proved extremely useful for calibration 
purposes as well as for secondary standards. 


CONFIDENTIAL 















































MEASUREMENT OF TRANSDUCER PERFORMANCE 


19 



20 22 24 26 28 30 32 34 36 38 


FREQUENCY IN KC 

Figure 21. Tr:in.smitting respoii.se of magiietostrictive unit. 



20 22 24 26 28 30 32 34 36 


FREQUENCY IN KC 

Figure 22. Receiving response of magiietostrictive transducer. 


1.18 MEASUREMENT OF TRANSDUCER 
PERFORMANCE 

Details of the measuring technique will not lie 
considered here. Simply to illustrate the various 
relations deduced in the preceding sections, the 
results of measurements on an experimental magneto- 
strictive unit are presented in Figures 21 and 22. 


The unit is sketched in Figure 23. It consisted of 
four stacks of nickel laminations 0.010 inch thick. 
Each stack was 3 inches high and was polarized with 
permanent magnets. From Figure 22 and from 
iinjicdance and pattern measurements, the following 
data are taken: 

Resonant frequency = 27.2 kc. 

Zt (elements in series) = 102 + jlGO (ohms). 


CONFIDENTIAL 












































































2(» 


INTRODUCTION 


Sensitivity at resonance = — 77.8 db ref 1 volt 
per dyne per sci cm (all elements in series). 

The value of D computed from pattern measure¬ 
ments was 0.0157. 

The efficiency calculated from these data, using 
ecpiation (25a) is —3.6 db = 0.43. 

The efficiency at resonance may also be comijuted 
from data obtained by driving the unit as a pro¬ 
jector (.see Figure 21). In this ca.se, the four ele- 

STAINLESS - STEEL CAN 



CONSOLIDATED STACK OF .OlO" 

annealed nickel laminations 

3''HIGH 



RUBBER RADIATING FACE 


SINTERED OXIDE 
(LOOSE FIT, NO CEMENT) 


AIR-CELL NEOPRENE 
PRESSURE RELEASE 
LINING TO CAN 


STAINLESS-STEEL 


AIR-CELL NEOPRENE 
PRESSURE RELEASE 
UNDER WINDINGS 


22 TURNS PER LEG OF 
«22 SCE MAGNET WIRE 


RUBBER SEALING 
TAPE 


Figure 23. Sketch of ma^netustrictive transducer. 


ments were connected in itarallel. The measured 
(juantities needed for this computation, using ecpia- 
tion (20) were as follows: 


errors, although fairly small when expressed in 
decibels, are large numerically, differences as great 
as 3.0 decibels (or a factor of 2 to 1) may reasonably 
l)e expected to appear, unless all mea.surement.s are 
made with extreme care and under the best experi¬ 
mental conditions. 



Figure 24. Effect of termination on receiving re¬ 
sponse of traiLsducer. 


l.lh BAM) WIDTH: .SHARPNESS OF 


RESONANCE 


20 log p' = 85.2. 

r = 2.36 meters. 

Z, = 6.4 4- JIO (ohms). 

, \ E \ 

Driving current / = | ^ | = 1.0 ampere. 

The efficiency computed from equation (20) is 
— 4.3 db = 0.37. It .should be said that the agree¬ 
ment in the comiiuted values of the efficiency from 
receiving and transmitting response data is better 
than is usually found in comiiari.sons of this sort. 
Because of the number of factors involved in each 
of the two eciuations and the fact that measurement 


As has already been stated, the various freciuency 
response curves of a resonant transducer will show 
jieaks at or near mechanical resonance. It is cu.s- 
tomary to s])eak of the liand width as the interval 
between the two frtHiuencies at which the respon.se 
has fallen to '\/l/2(= —3 db) relative to its peak 
value. It should be emphasiztMl that the .several 
respon.ses which have been defined here may show 
large differences with respect to band width, both in 
magnitude and in dependence on frequency. The 
situation is illustrated in Figure 24, where \'oltage 
sensitivities are shown for a particular transducer 


CONFIDENTIAL 















































BAND WIDTH: SHARPNESS OE RESONANCE 


21 


with several electric terminations. The band width 
may be expressed as the frequency interval or as a 
fraction by taking the ratio of the interval to the 
central frequency. By analogy with the current- 
voltage relation in a simple resonant circuit, it is 
common to speak of the Q of the response curve as the 
reciprocal of the fractional band width. Thus 


where /2 and /i are the “ — 3 dl) points” and /o = 
fif I is the center frequency. As can be seen from 


Figure 24, the Q ranges from 7.2 to 13.5, depending on 
which of the respon.ses mea.sured is used in equation 
(33). Care must therefore be taken to specify the 
conditions of measurement of the response in quoting 
a Q determined in this way. 

In addition to the foregoing sending and receiving 
data needed for the intelligent use of transducers 
designed to serve both as projectors and hydro¬ 
phones, special types call for other kinds of measure¬ 
ments. It is also possible to secure much useful 
information on transducer performance from the 
purely electric measurements covered in Chapter 11. 


CONFIDENTIAL 




Chapter 2 

TRANSDUCERS AS MULTITERMINAL NETWORKS 


2.1 ELECTRIC SYSTEMS 

In aiiproaching the theoretical treatment of mag- 
netostrictive transducers, a purely electric four- 
terminal network as shown in Figure 1 is considered. 
The network is as.sumed to be compo.sed of linear 
passive elements. Then the relations between the 
potentials and currents on the two sides of Figure 1 
can be written (see glossary for definitions) 

El = Zili + Z 12 I 2 , /.s 

E 2 = Z 21 I 1 + Z 2 I 2 , ^ ^ 

with 

Z1Z2 — Z12Z21 7^ 0 . 

The impedances Zi and Zt are the impedances on 
the two sides when the opposite circuits are open, 
whereas Z 12 and Z 21 are known as mutual impedances. 
For a purely electric system with linear passive ele¬ 
ments, the reci{)rocity theorem states that 

Z 12 = Z 21 . ' (2) 

If the network of equation (1) is to be physically 
realizable with passive elements, the resistive parts 
of Zi and Z 2 must be positive, although there is no 
such condition on Z 12 . Thus, 

Zi = Ri + yXi Ri ^ 0, 

Z 2 = /f2 + jX2 ^ 0, (3) 

Z12 = ifl2 + jXl 2 - 

An application of the network is in transferring 
power from a source to a load as shown in Figure 2. 
Then, in addition to equations (1), 

E 2 = -ZJ 2 , (4) 

and by eliminating E 2 and 1 2 between equations (1) 
and (4) it is found that the input impedance w ith the 
load connected is 

Zi = Ri+jX, = Z: - ^ • (5) 

^2 “T 

The efficiency of the four-terminal netw’ork (the 

ratio of the pow'er output at terminals 2 to the 
power input at terminals 1) is 


Efiuation (6) has a maximum with respect to A'/, 
when 

Ri{X2 + Xl) ~~ R 12 X 12 = 0, (7) 



and a maximum with respect to Rl when 

R'lRl = (R 1 R 2 - Rl 2 )iRiR 2 + X%) (8) 

“b + X l) ~ /fl 2 A’^i 23 “- 


If equations (7) and (8) hold .simultaneously, the 
value of equation (6) is 


VR 1 R 2 + X'i, - VR 1 R 2 - /4 
's/RiR 2 + A" 12 “b R 1 R 2 — Ri 2 


(9) 



Figure 2. Four-terminal network connected to load, 
— Rl —JXl- 


The potential efficiency is thus the highest efficiency 
that a four-terminal network can exhibit in trans¬ 
ferring power from one pair of terminals to the other 
when both the resistance and the reactance of the 
load are considered variable. 

It can be showm that the necessary and .sufficient 


Eff = 


Rl 

R. 


Z 12 2 

Z 2 “b Zl 


_ RiRLiR'h + XI2) _ 

[/?i(/?2 + Rl) - /4][/?i(^2 + Rl) + Ay -b [Ri{X2 + Az.) - /?i2Ai2?’ 


(b) 


22 


CONFIDENTIAL 




























FI.KCTROMECnANICAL SYSTEMS 


23 


condition that must l>e satisfied if ecjuation (6) is 
to remain less than unity for all Z^, with ^ 0 is 

RiRo - R\., ^ 0. (10) 

This equation must be satisfied by any four-terminal 
network which is made up of linear, passive, physi¬ 
cally realizable elements. The ecjuality in ecjuation 
(10) sives a maximum efficiency of unity accoi'ding 
to eciuation (9). 

It is interesting to compare equation (10) with 
the equations satisfied by special types of four- 
terminal networks. Con.sider, for example, the T 
network shown in Figure 3. It is easily found that 

o- |Za = Ra + jX^[ — Rc + jxcl -o 


Ie i^BI 

o--o 

Figure 3. T network. ' 

the impedances of equations (1) are related to those 
of Figure 3 by the equations 

^1 = ^.4 + 

Z 2 = Zji + Zc, (11) 

Z 12 = Z 21 = Z/j. 

To be physically real the elements of the T network 
must satisfy 

Ra ^ Q, Rn^ 0, Rc ^ 0. (12) 

Hence, from eipiation (11), 

Ri ^ Ri2, (13) 

Ri ^ ^12- 

Equation (10) is, therefore, .satisfied by the T net¬ 
work, but note that the conditions in equation (13) 
are stronger than in (10). Thus not all physically 
realizable four-terminal networks can be obtained as 
T networks. It is quite easy to find, for example, a 
feasible w network which can be represented by a 
T network only with the help of negative re.sistance 
elements. 

2.2 ELECTROMECHANICAL SYSTEMS 

Linear passive four-terminal networks are con¬ 
sidered (Figure 4) in which two of the terminals are 
electrical and two mechanical. In the figure, F is 
the force of the (water) load on the radiating surface 


of tlie tran.sducer, while v is its velocity. The con¬ 
vention on directions is such that the transducer is 
receiving energy from the load when F and v are in 
phase. Ecjuations (1) hold for the electromechanical 
network if appropilate changes are made in the 
impedances. 

E = ZJ + Z^v, 

F = Z„T -b Z„,B, (14) 

Z,Z„, ZeviZme 9^ 0. 

In equations (14), Z^ = 7?^-f-jAT is the electric 
impedance of the electromechanical transducer or 
network when the mechanical side is rigidly clamped 


I , _ V 




■* 


t 


t 


E 

1 

Ze Zem 

F 

1 

Zl 






Figure 4. Electromechanical four-terminal network 
of transducer with attached mechanical load. 


{v = 0), and Z„, is the mechanical impedance (F/v) 
of the transducer when the electric terminals are 
open-circuited. The electromechanical mutual im¬ 
pedances are Zf„. and Z^e- The system is taken to 
involve only one type of electromechanical coupling. 
Then a reciprocity theorem holds for the system and 
Zem = + Zme accoi'diiig to the type of coupling; 

Z,.m = + Z,„,; (electrostatic or piezoelectric cou¬ 
pling). (15) 

Zem = — Zme (electi’omagnetic or magnetostric- 
tive coupling). (16) 

A system incorporating types of coupling correspond¬ 
ing to both (15) and (16) may not .sati.sfy the reci- 
I)rocity theorem.®* 

With electrostatic or piezoelectric coupling, equa¬ 
tion (15), the analy.sis of equations (3) to (13) ap¬ 
plies, if the obvious changes in subscripts are made. 
On the other hand, for electromagnetic or magneto- 
strictive coupling, when equation (16) holds, some 
further changes must be made. The rest of this 
section is restricted to this case. By rewriting 
equation (14) and employing equation (16) it is 
found that 

E = Zel -b ZemV \ electromagnetic or 
F = —ZemI + Zmvj magnetostiictive (17) 
ZeZm + Z“„, 0. 

“ For a linear transducer system that does not satisfy the 
reciprocity system, see reference 1. 


CONFIDENTIAL 





















24 


TR ANSDUCERS AS MULTITERM INAL NE:TW0RKS 


As before, for a physically realizable passive system 

Z, = R, + jXe, Re ^ 0, 

Z„ = Rm+jX^, (18) 

Zem = Rem +iA,m. 

Since the mechanical load in Figure 4 has impedance 
Zl^Rl+JXi., 

F = -Zj,v, (19) 

and the electric input impedance with the mechanical 
termination is 

Z.- = Ri + jXi = Z, + ( 20 ) 

The efficiencj' of the transducer in converting electric 
power into mechanical power is then 


/?. ' Z„, + Zi 


( 21 )” 


The maximum of equation (21) with respect to Xl 
occurs when 


Re{X^ + Xl) + RemX^ = 0, (22) 

and that with respect to Rl when 

RlRi = {ReRm + RL)(RMm - A'L) 

+ iReiXm + A'z.) + RemXemJ. (23) 


The value of equation (21) at the maximum with 
respect to both \’ariables is 


VReRm + R'L - VReRm - 

VRMm + RL + V R,R^ - A^„. 


(24) 


The potential efficiency is the highest efficiency that 
the four-terminal electromechanical network can 
exhibit in transferring power from its electric to its 
mechancial terminals or vice versa. The nece.ssarv 
and sufficient condition that potential efficiency al¬ 
ways remain less than unity is 

ReRm - AL ^ 0. (25) 


It will be noticed that the only difference between 
equations (10) and (25) is exchange of real and im¬ 
aginary parts of the mutual impedance. 


2.3 EXAMPLE — LOUDSPEAKER 

The preceding general theory will be illustrated by 
an application to an electromagnetic transducer or 
loudspeaker of the dynamic type. The essential 
components are shown in Figure 5A. 


The cone assembl^y is taken to be perfect!}' stiff, so 
that the motion is everywhere the same and lumped 
constants can be used. The system has a mass M, 
a stiffne.ss K, and a certain internal mechanical 
damping resistance Rm which does not include the 
ratliation load. The voice coil consists of N turns of 



Lg 



Figure .5. .A. Dynamic-type loudspeaker, li. Equiv¬ 

alent circuit of loudspeaker. 


radius a with a resistance Re and inductance 
The induction in the gap where the coil lies is B. The 
force F is aitplied on the system by some external 
mechanical agency, .such as air, and the positive 
direction of v is the same as for F. An alternating 
potential E is applied to the terminals of the coil and 
a current I flows through it. For definiteness, it is 
a.ssumed that a positive current circles the coil in the 
counterclockwise sense when viewed from the front 
of the speaker (top of f’igure 5A). 


bEff = 


Rl 


Ze 


Zm + Zl, 


RRAR -f A'2 ) 

e ^ L'' em ' em' _ 

+ Fj) + R'l^'MReiFm + R 0 “ + IR J.X^ + A'J + Rem^ 


COXFIDENTIAL 

































EX\MP[,E — LOUDSPEAKER 


25 


In the following, unless otherwise stated, electric 
units are measured in the electromagnetic system. 
The reason for this is that the practical system of 
electric units uses the watt as the unit of power, 
whereas the cgs power unit is the erg per second 
(= 10“’ watt). The reciprocity theorem in the .simple 
form of equations ("15) and (16) holds only when the 
electric and mechanical power units are the .same. 

Let the .system he acted on by an applied force F 
of which the angular frequency is w, with the coil 
open so that no current hows. Then motion takes 
place with velocity v given by 


F = Z„,v = 


+ - + /?„ 


(26) 


If a current I Hows through the voice coil and it is 
required that the same motion be maintained, an ad¬ 
ditional force must be applied. This is equal and op¬ 
posite to the force produced on the coil by the interac¬ 
tion of I and B and can be calculated without regard 
to the motion of the coil. Then 


F = -2TaNBI + Z,nV, (27) 


with the mechanical impedance Z„ as in equation 
(26). 

On the other hand, it is po.ssible to start from the 
electric side and apply a potential E to the coil, with 
the .system clamped mechanically so that its velocity 
is zero. Then a current I flows, given by 

E = ZJ = (K, + jo:Le)L (28) 

If now the coil is allowed to move with velocity v 
and the same current must be maintained, then E 
must be altered by the emf generated in the coil by 
the motion. Then 

E = ZJ + 2TaNBv, (29) 


with the electric impedance Z^ as in equation (28). 
Equations (27) and (29) are of form (17) with 

Z,„ = 2wnNB. (30) 


2.3.1 Two-Terminal Equivalent 
Circuit of Loudspeaker 

In normal operation the loudspeaker is fed electric 
power and radiates acoustic power. The normal load 
Zl (see Figure 4) is thus the radiation impedance of 
the air to the cone. For simplicity, a.s.sume that 
this is a pure resistance Rl- The electric impedance 


seen at the coil terminals is given by ecpiation (20) 
and can be written 

r 7 , ■ r 47rW’a"fi- y 

Zi = Re JOlLe 4-(31) 

RmJ Rl+ + ^ 

With tlie help of the abbreviations 

■iir'N-a-B- 4irW-a“fi'’ 

Rl = -;;- , Rl - 


Rl 

M 


R„ 

AirN~a-B- 

K ’ ' 47rW2a'W- 

ecpiation (31) can be written as 

Z^i = Re joiLe 4—J j j— 

“ + ^ 4- iwCi 4- 
Ri R2 j<^Li 


(32) 


(33) 


The impedance at the electric terminals of the loud¬ 
speaker is thus the same as the impedance of the cir¬ 
cuit shown in Figure 5B. The series elements Re, Le 
are purely electric, whereas the shunt elements /fi, 
Ri, Li, and Ci are the elements reflected into the elec¬ 
tric circuit by the mechanical system. When the 
mechanical impedance is made very large, as by 
blocking the cone, the shunt impedance becomes very 
small and the impedance reduces to that of the electric 
elements alone. The additional impedance due to 
the mechanical .system is known as motional imped¬ 
ance, designated Z,not. From equations (20) and (33) 


Zmot — Z i — Ze — 


Z„, -b Z, 

1 


(34) 


■^4- 4- iwCi 4- . j 

Rl R 2 


2 . 3.2 Impedance Diagram 

In this work it will often be found convenient to 
plot an impedance such as the motional impedance 
(34), regarding Zn,ot =-Rmot + A"mot as a vector 
with horizontal and vertical components Rmot and 
respectively. Since Z^ot is not constant but 
depends on the frequency, it will plot out a locus as 
the frequency is changed. This locus will be spoken 
of as the impedance diagram. In the particular case 
of equation (34), it will now be shown that the 
motional impedance diagram is a circle, as pictured 
in Figure 6. The easiest way to do this perhaps is 


CONFIDENTIAL 













26 


TR ANSDUCERS AS MULTITERM INAL NETWORKS 


to put equation (34) into polar coordinates. The fol¬ 
lowing abbreviations are used: 

^ -D\^\ 

+ R'd {Rm Rl) ' Li (35) 

I K 1 1 / W COo 

Then equation (34) becomes 



Zmot — ^ i ~ Zf — 


D 


1 +j2Qp 


(36) 


L| 



The quantity p measures the departure of the fre¬ 
quency from resonance, which occurs when w = wq. 
At resonance the motional impedance is a pure re¬ 
sistance equal to D. To convert (36) to polar 
coordinates p, 6, note that 

tan e = ^ = -2Qp, 

n 

p= Vr-^ + X'^ = - 

VI -t- 4QY- 

By eliminating 2Qp between these two equations, 
p = D cos 6, (38) 

which is the polar equation of the circle with diam¬ 
eter D shown in Figure 6. As the frequency increases 


from zero, the impedance locus, starting at the 
origin, traces out the circle in the clockwise sense 
indicated by the arrow, finally returning to the 
origin when the frequency becomes infinite. 

Resonance occurs at the frequency /o(= wo/Stt) 
where the circle crosses the resistance axis. The 
diameter joining the origin with the point/o is known 
as the resonance diameter. The points marked with 
the fre(}uencies/i and /2 are of special interest. The^y 
lie at the entls of the diameter perpemlicular to the 
resonance diameter. At the.se points, 6, the phase 
angle of the impedance, is ± 45°, and p, the magni¬ 
tude of the impedance, is of its maximum value 
D at re.sonance. These are also sometimes known as 
the 3 db points, since a constant current through 
the circuit will develop across it a voltage 3 db le.s.s 
at/i or /2 than its value at/o. It is ea.sy to show that 
/ 1/2 = /o, so that /i, fo, and are uniformly spaced 
on a logarithmic scale. The relation 


Q = 


/° 

(/2 - / l ) 


(39) 


is easily deduced. 

As has been stated earlier, the blocked impedance 
is the impedance due to the purely electric elements 
and is given l)y 


Ze — Re j<^Le. (40) 



Figure 7. Blocked imiiedance diagram. 


The impedance diagram for equation (40) is shown 
in Figure 7. The locus is a straight line, parallel to 
the reactance axis and Re to the right. Frequency 
increases upward along the line,/ = 0 being the point 
on the resistance axis. The point fo lies at the 
height A'o = woLe = 27r/o/>e, with similar formulas 
for/ 1 ,/ 2 . 


CONFIDENTIAL 





























EXAMPLE — LOUDSPEAKER 


27 


The total impedance as given by equation (33) 
is the vector sum of the blocked and motional imped¬ 
ance and can be obtained by combining Figures 
6 and 7. The result is shown in Figure 8. 

The measured impedance of a small permanent- 
magnet loudspeaker (Utah 4PZ), suspended in air 
without baffle, is shown in Figure 9. It will be 
noted that the observed curve has the same general 
characteristics as the theoretical one. In Figure 9 
the motional impedance is somewhat larger, com¬ 
pared with the blocked impedance, than that as¬ 
sumed in drawing Figure 8, so that the impedance 
becomes capacitive over a range of frequencies. 


X 



Figure 8. Total impedance diagram. 


From Figure 9 the following set of values can be 
deduced: 

i?e = 3.0 ohms, 

Le = 150 ;uh, 

D = 3.5 ohms, 

/o = 234 c, 

/i = 214 c, (41) 

/2 = 256 c, 

Q = 5.6 
Li = 425 Mb, 

Cl = 1090 Mf. 

The assumptions made and the data obtained are 
not .sufficient to determine the efficiency. However, 
a formula can be derived that will be instructive 
for later applications. Consider formula (21) as 
applied to the present case. In the first place, 
according to equation (30), is real, so that 
Xem = 0. Now, as the frequency is varied, the 
only term in (21) which changes is -|- Xl- Ac¬ 
tually it has been assumed that Al = 0, but in any 


case X„i and Xl can be lumped. Also Rl is assumed 
to be constant. Then the maximum of efficiency 
with respect to frequency is the maximum with 
re.spect to A'„,-|-A/,, as given by equation (22). 
Since Xem = 0, this maximum occurs at /o, the fre¬ 
quency of resonance. From equation (21) its 
value is found to be 


Eff 


resonance 


1 _ Rl 

RejRm + Rl) ~\ ' Rm + R L 

R'L -I 


(42) 


Comparison of equations (30), (32), and (35) shows 
that 


Rm + Rl 

RL 


1 

d' 


(43) 


where D is the diameter of the motional impedance 
circle. Equation (42) then becomes 


Eff 


resonance 


D Rl 

Re -\- R Rm R L 


(44) 



2 3 4 5 6 7 

R IN OHMS 


Figure 9. Measured impedance of 4-in. PM speaker 
(Utah 4PZ). 

So far, no way of obtaining the second factor in this 
equation has been proposed. This will be tem¬ 
porarily disregarded here. The first factor, however, 
can be directly found from Figures 8 or 9. In the 
latter, it is equal to 0.54. The two factors in (44) 
can be given a very .simple interpretation. The 
first factor can be regarded as a gross electromechan- 


CONFIDENTIAL 












































28 


TKANSDUCKRS AS MUL1ITERMFNAL NETWORKS 


ioal conversion efficiency whereas the second can l)e 
thought of as a purely mechanical efficiency which 
gives the fraction of total mechanical power that 
the speaker delivers to the useful load (radiation 
resistance of air). It is seen that both factors are 
less than unity, so that the above interpretation is 
reasonable. A word of caution is nece.ssary, how¬ 
ever, since later transducers will be considered in 
which the equivalent of the first factor may exceed 
unity, although the product of the two never does. 

2..8.3 Four-Terminal Equivalent 
Circuit for Dynainie Speaker 

The circuit already obtained in Figure 5 is equiva¬ 
lent to the speaker as a two-terminal electric net¬ 
work; that is, the circuit represents correctly the 
reflection into the electric circuit of the ma.sses, 
stiffnes.ses, and resistances which are jiarts of the 
speaker or coupled to it. It cannot be seen from 
the circuit just what the velocity of the cone is when 
a known voltage is applied nor what force is de¬ 
veloped between the cone and the air. The circuit 
does give the correct disposition of power among 
internal electrical and mechanical losses and use¬ 
ful radiation, and this information is frequently 
.sufficient. 

However, .slightly more complicated equivalent 
circuits can be constructed which represent the loud¬ 
speaker as a four-terminal network, so that force 
and velocity appear at the mechanical terminals as 
well as voltage and current at the electric terminals. 
The mutual impedances have already been shown to 
be of opposite sign in an electromagnetic or magneto- 
strictive system and of the same sign in electrostatic, 
piezoelectric, and purely electric .systems. It is clear, 
therefore, that an electric four-terminal network 
cannot be obtained equivalent to an electromagnetic 
or magnetostrictive system, when force is replaced 
by voltage and velocity by current. However, by re¬ 
placement of force by current and velocity by voltage, 
such a representation can be made. By rewriting 
equations (17) to obtain E and v as linear combina¬ 
tions of I anti F, 



Notice that the cro.ss coefficients are now equal not 
only in magnitude but also in sign. Thus, if F is 


regarded as a current and as a voltage, a purely 
electric network equivalent to equations (45) can 
be formed. The simplest is shown in Figure 10, 



Figure 10. Equivalent four-termin.al network for 
electromagnetic transducer. 

where the transformer .shown is ideal with impedance 
ratio to unity. If a resistance 1/Rl is connected 
acro.ss the mechanical terminals, with the help of 
etpiations (30) and (32) it is found that Figure 10 
becomes the same as Figure 5. With Figure 10, of 
course, the current (force) flowing in and the voltage 
(velocity) developed across the mechanical load can 
be determined. 

Consider a simple example of the use of Figure 10, 
here using low frequencies, for which the wave length 



Figure 11. Equivalent circuit of dynamic speaker at 
low frequencies. 

is greater than the circumference of the speaker con¬ 
sidered as a vibrating disk. It can be shown then 
that the load to be connected to the right termi¬ 
nals in Figure 10 consists of a resistance and con- 



Figure 12. Equivalent circuit of dynamic speaker at 
intermediate frequencies. 

denser in series, in order to represent the radiation 
impedance of the air. This is equivalent to insert¬ 
ing a condenser in series with R 2 in Figure 5, jdeld- 
ing the circuit of Figure 11. 

The symbols used are for the most part the same 


CONFIDENTIAL 




















IMOnONAL IMPEDANCE 


29 


as in Figure 5. When the speaker is driven elec¬ 
trically, power dissipated in represents useful 
radiation of sound. For further restriction of the 
freciuency range, consider only frequencies above 
re.sonance. Thus for the speaker whose impedance 
was shown in Figure 9,^ frequencies are limited to 
those between 400 and about 1,500 c. In this 
range the circuit reduces to Figure 12, where the 
omitted elements are negligible. Furthermore, the 
^■arious impedances are related bj' 


Re>> 


jwC] 




and thus the power delivered to K 2 (useful radiation) 
is approximately 

/E icoC-V 

Railiated ])ower = (-) R 2 , 

' \Re jc^Cj ’ 

which is independent of frequency. 


2.4 MOTIONAL IMPEDANCE 

Before an explicit consideration of magnetostric¬ 
tion is developed, some of the results already found 
for the dynamic loudspeaker will be generalized. 
[Methods will be obtained by which the impedance 
and particularly the motional impedance of a trans¬ 
ducer to operate in water can be used to determine 
its potential and actual efficiency. 

As already stated, the motional impedance of a 
transducer is that part of its electric impedance ari.s- 
ing from the motion of its mechanical terminals. 
In representing the motional impedance by Z^ot) 

can be written, as in equation (34). 

In this equation, Z,- and Z^ are impedances meas¬ 
ured at the electric terminals, the first when the 
transducer is free to move under mechanical load Zi, 
and the second when the transducer is blocked so 
that no motion is possible at its mechanical terminals. 
The second equality in equation (46) comes from 
the previous expression (20) for Z,. According to 
equation (46), the motional impedance is the vec¬ 
tor tlifference between the loaded and blocked im- 
l)edance. If the loaded and blocked impedances 
have been measured and plotted as two curves in an 
impedance -diagram, the motional impedance can 
immediately be determined through a point-by- 
point subtraction of the two curves. 


Frequently in underwater .sound, the mechanical 
system, consisting of the mechanical jjarts of the 
transducer and the load, is resonant at some fre¬ 
quency. Usually, if this resonance is pronounced, 
the tran.sducer is useful only in a certain frequency 
range near resonance. The methods to be developed 
in this section are particularly useful for re.sonant 
transducers and get into difficulty in application 
when the mechanical resonance becomes very broad. 
The total mechanical impedance (internal plus load) 
will be assumed to be resonant at the frequency /o. 
When the frequency is in this vicinity this imped¬ 
ance will be written in the usual form 


Zm + Zi — {Rm -j- Rl) j\^M 



(47) 


Here /?,„ (internal) and Rl (load) are mechanical re¬ 
sistances, M is the equivalent lumped mass, and K 
the equivalent lumped stiffne.ss of the .system. These 
quantities, Rl, M, and K, are constant over the 
interval to which equation (47) applies. The angu¬ 
lar frecpiency wo at resonance is given by 


Wo = Stt/o = 



(48) 


Just as in electric systems, it is convenient to de¬ 
fine a mechanical Q which mea.sures the .sharpness of 
mechanical resonance and may be taken as the 
ratio at resonance of the mass or stiffne.ss reactance 


to the resistance; 

Q - - 

^ (R^ + Rl) 


(49) 


The total mechanical impedance (47) may now be 
rewritten 


Z,„ + Zi = {R„, + Rl)LI + i2Qp], (50) 
where, as in equation (35), the abbreviation 



has been used. 

The frequencies at which the phase angle of 
Zm + Zl is ± 45° are/o and/i, and the relations 

M = Q = (52) 

(,/2 — Jl) 


exist. The motional impedance can now be written 
as 


= Zi- Ze 


1 


Rm + RL [l+i2Qp] 


(53) 


CONFIDENTIAL 









30 


TRANSDUCERS AS MULTITERMINAL NETWORKS 


which is very similar to the motional impedance 
found in equation (36) for the loudspeaker. The 
only difference is that there the coefficient D was 
real, whereas here the coefficient + Rl) in 

general is complex. Assume that Zem is independent 
of frequency or at least that it varies slowly enough 
compared with Zm + Zx, so that it can be considered 
constant in the neighborhood of resonance. Then 
the motional impedance (53) is a circle whose 
resonance diameter is inclined to the horizontal at 
an angle equal to twice the phase angle of Z^^, and 
whose diameter is 


D = 


\ZL\ 

(/?m + Rl)' 


(54) 


The motional impedance circle is illustrated in 
Figure 13 for the case where Zem has a small negative- 
phase angle. It will be noticed that the re.sistive part 
of the motional impedance is negative over a certain 


X 



Figure 13. Motional impedance of a resonant trans¬ 
ducer. 


part of the impedance circle in Figure 13. This does 
not represent a violation of energy conservation, 
however, since condition (25) insures that total 
input resistance Ri and clamped electric resistance 
Re are always positive. 

Equations (49) and (54) give the mechanical Q 
and the diameter of the motional impedance circle 
when the transducer is loaded with the mechanical 
resistance Rl- When the transducer is placed in 
water, Rl is the radiation resistance of the water to 
motion of the face of the transducer. A subscript 
IF on Q and D will be used to denote that these 
quantities are measured with the normal radiation 
load of the water on the transducer. 


Similarly, if the transducer is removed from the 
water and measured in air, the radiation load Rl is 
effectively zero. The subscript A will be taken to 
denote measurements of Q and D made under these 
conditions. Note that the same formulas, (49) and 
(54), giv'e both Qw and Qa, and D^y and Da; Rl is 
set equal to zero when the transducer is in air. In 
general, Zl, the radiation impedance of the water, 
will not be a pure resistance. There will then bo 
differences in M and K between measurements in 
water and air. The most noticeable effect will be a 
change in the frequency of resonance, as given by 
(48), between air and water. Whenever the dimen¬ 
sions of the transducer are large in comparison with 
the wave length, the radiation impedance will be 
almost purely resistive and change in re.sonance will 
not occur. 


2.4.1 Efficiency at Resonance 


The efficiency of the transducer, which was given 
by equation (21) can be rewritten with the use of 
equation (20) in the form 


Efif = 


Z. - Z, 
Ri 


Rl 


Zm+Z, 


(55) 


At resonance, | Z; — Z^ | becomes equal to Dfy, the 
diameter of the motional circle in water. Further, 

I Zm + Zl I becomes Rm + /?u, in accordance with 
equation (47). Also, from eciuation (54) 


Rl _ Da — D\y 
Rm + Rl ^ 

Thus, the efficiency at resonance becomes 

_ Rn\ 

R. V Da/’ 


(56) 


(57) 


where Ri = resistance at resonance in water, 

D^7 = diameter of motional circle in water. 
Da = diameter of motional circle in air. 

The first and second factors in equation (57) 
may be interpreted respectively as a gross electro¬ 
mechanical efficiency and a pure mechanical effi¬ 
ciency. The separation into electrical and mechan¬ 
ical losses is not unambiguous, however, and it is 
possible to have the first factor greater than unity, 
although the product is always less. 


CONFIDENTIAL 










MOTIONAL IMPEDANCE 


31 


2 . 1.2 Potential Efficiency 


The potential efficiency of an electromechanical 
transducer is its maximum efficiencj^ in converting 
electrical to mechanical power, when both the 
mechanical load resistance and reactance are varied. 
The expression (24) has already been deduced for 
this quantity; however, it depends on quantities 
not directly known or measurable. The following 
formula is one from which, in a great many cases, 
the potential efficiency can be found at once from 
impedance data. 

Ecjuation (24), rewritten with slight alteration, 
gives 


Pot eff 


Re + 


Ri 


- V Re - 


x: 


Re + 


R„ 


+ 




(58) 


X 



Figure 14. Impedance diagram for transducer in air. 


Consider now the impedance diagram for the 
transducer in air. The diameter of the impedance 
circle, obtained from equation (54), is 


Da 


z'L 


{Rjm + X\^ ^ 

Rm 


(59) 


since Zem = Rem + jXem- In general, Rm is several 
times smaller than Rm Rl- Thus the diameter of 
the air circle is several times larger than the water 
circle and, in addition, the resonance in air is sharper 
than in water. These facts frequently combine to 


make it a good approximation to a.ssume that the 
blocked impedance is constant while the motional 
impedance is traversing the greater part of the circle. 
The impedance diagram is shown in Figure 14 and 
con.sists simply of the motional circle displaced by 
the constant Ze. As noted after equation (53), the 
inclination of the resonance diameter is 2^em, or 
twice the phase angle of Zem and it is found from 
simple geometrical considerations (when blocked 
impedance may be considered constant) that 


^max = + ^[1 + COS 2f,„] = Re + Da COS' 

Rmin = - ^[1 - COS 2C,J = Re “ Da sin^ ^em, 

(60) 


where R^^x and R„An are the maximum and minimum 
resistances around the circle, as shown in Figure 14. 
From equation (60) and the fact that 


tan ^em = 


D _ 7? 4- 

^max I f 


(61) 


7? = 7? — 

O-min ^e 


These are just the quantities needed for the po¬ 
tential efficiency in equation (58). Thus, finally, 

a / t ? —y/R 

A re /con 

Pot erf = /— -7= • (62) 

Vff + Vi? • 

As already stated, the principal condition for the 
validity of equation (62) is that the blocked imped¬ 
ance can be considered constant over the motional 
loop. This implies that the motional loop is very 
close to a circle. 

Equation (62) is verj^ easy to apply and gives a 
figure of merit for the transducer without requiring 
measurements in water. 


2.4.3 Application to Actual 
Transducer 

The idea of motional impedance and its represen¬ 
tation by the motional impedance circle can best be 
illustrated by data obtained from measurements on 
an actual transducer. In Figure 15 are shown im¬ 
pedance diagrams for a stack of nickel laminations. 


CONFIDENTIAL 


















32 


tuansi)U(:f>:rs as .multitkr.minal networks 


jiunched in the form of circular rings from 5-mil 
sheet and wound toroidally. The total reactance Xi 
is plotted against the total resistance Hi for both air 
and water measurements, over a range of frequencies 
including resonance. The characteristic loop pro¬ 
duced by the motional impedance is evident. The 
loops are not perfect circles, since the blocked 
impedance is not strictly constant over the frequency 
range corresponding to the major portion of the 
loop. 


The transducer illustrated in Figure 15 is par¬ 
ticularly favorable in this respect since both loops 
are close to circles, implying rather small changes in 
the blocked impedance. The loops are flattened 
slightly in the direction of the change in the blocked 
impedance, which is appro.ximatel}^ the direction of 
a line drawn between points at 30 kc and 80 kc. The 
diameters of the air and water circles may be esti¬ 
mated from Figure 15 with reasonable accurac}'; 
thus. Da = 7.8 ohms, D^- = 2.35 ohms. In adtli- 


cn 

2 

X 

o 

z 

X 



0 2 4 6 8 

R IN OHMS 



0 12 3 

R IN OHMS 


AJN AIR 

Figure 15. .\ir and water impedance diagrain.s. 


B,IN WATER 


It is not feasible to try to obtain the blocked im¬ 
pedance by direct measurement on a transducer for 
use in water, since it is virtually impossible to find 
a large enough mechanical load Zl- What must be 
done is to estimate the blocked impedance bj" inter¬ 
polation between two frequencies sufficiently above 
and below resonance so that the motional impedance 
can be assumed small. Various procedures are 
available, but it is clear that the accuracy with 
which the locus of the blocked impedance can be 
estimated and the accuracy with which the motional 
impedance can be determined will dejiend on how 
much the blocked impedance changes over the 
greater part of the motional loop. 


tion, the resistance in water at resonance is about 
2.9 ohms. The last figure is less certain, since the 
point of resonance has not been located accurately. 
By use of equation (57), 0.57 is found to be the 
efficiency at resonance. The maximum and mini¬ 
mum resistances in Figure 15A are 8.1 and 0.5 ohms. 
The potential efficiency determined from equation 
(62) is therefore 0.60. 

When the blocked impedance changes more rapidly 
with frcciuency compared with the motional imped¬ 
ance than it does in the present example, it is nece.s- 
saiy to obtain the motional impedance explicitly. 
Far enough from resonance, the motional impedance 
will be small, so that the blocked and total imped- 


CONFIDENTIAL 






















































MOTIONAL IMPED\NCE 


Xi 


v> 

S 

I 

o 

z 


X 

o 

z 

< 

a: 



Figure 16A. Resistance and reactance of transducer in air. 



Figure IGB. Motional impedance diagram for trans¬ 
ducer in air. 


anee curves will come together. The course of the 
blocked impedance may, therefore, be estimated by 
drawing a smooth curve between a point well below 
and another well above resonance. The choice of an 
interpolation curve will be governed by the appear¬ 
ance of the impedance diagram and by theoretical 
considerations dependent on the nature of the tran.s- 
ducer. In Figure 15, good results are obtained if 
the blocked impedance is taken as a straight line 
with a uniform frequency scale joining the points at 


30 and 70 kc. Theoretically, the curve for this 
transducer should be the arc of a circle, as will be 
•seen in Chapter 3. Once the blocked curve has been 
chosen, the motional impedance is obtained by 
vector subtraction (graphically) from the total 
impedance. The success of the method is measured 
by the closeness of the motional loop to a circle. 


T.\bi,e 1 



.Air 

Water 

/(I 

56.2 kc 

53.6 kc 

Q =fo/{h-fi) 

33 

11 

D 

7.60 ohms 

2.34 ohms 

Re (resonance) 

0.52 ohm 

0.61 ohm 

A', (resonance) 

3.82 ohms 

4.00 ohms 

Ri (resonance) 

7.90 ohms 

2.90 ohms 

Ri (max) 

8.00 ohms 


Ri (min) 

Efficiency (resonance) 

0.40 ohm 

57% 

Potential efficiency 

63% 



A different interpolation method of somewhat 
greater complexity is shown in Figures 16 and 17. 
Here the total resistance i?, and reactance Xi are 
plotted against frequency for both air and water data. 
Interpolation curves, which in the present case are 
straight, are shown for the blocked quantities Re 
and Xe. Finally the components of the motional 
impedance are the differences Hi — Re and Xi — A'^, 
which are plotted as the circles in Figures 16 and 17. 
Pertinent data obtained from the curves are given in 
Table 1. 


CONFIDENTIAL 




































































34 


TRANSDUCERS AS MULTITER.MINAL NETWORKS 



30 35 40 45 50 55 60 65 70 75 


FREQUENCY IN KC 

A 

Figure 17A. Resistance and reactance of transducer in water. 


2.4.4 Motional Reactance at Reso¬ 
nance and at the Point of Maxiinuin 
Efficiency with Optiinuin Loading 

The motional reactance of a transducer at reso¬ 
nance in air, found from equation (53), is 

^Rem^em 

*^mot ~ „ ■ (h3) 

This is very simply related to the reactance of the 
same tran.sducer with optimum loading; and at the 
fre([uency which g;ives maximum efficiency (under 
the conditions for obtaining the potential efficiency). 
From equation (46), 

'^mot 

'2RemXem.{Rm + Rl) ~ {R]m ~ ^l) _ 

{Rm + RlY + A"l)" 

(64) 

\Mth the help of equations (22) and (23) it can be 
shown that equation (64) is 

R em^ em //»-\ 

A mot = —^- (bo) 



R MOTIONAL IN OHMS 

B 

Figure 17B. Motional impedance diagram for trans¬ 
ducer in water. 

Thus the motional reactance under optimum con¬ 
ditions for efficiency is one-half the motional re¬ 
actance at resonance in air. This fact will be used 
in Chapter 3 in discussing the geometry of the 
impedance diagram. 


CONFIDENTIAL 





































































Chapter 3 

MAGNETOSTRICTIVE VIBRATORS AND EQUIVALENT CIRCUITS 


3.1 EDDY CURRENT.S 


At ultrasonic fi'cquencies, losses due to eddy cur¬ 
rents in the masnetostrictive material may be quite 
large, even with laminated cores, and it is necessary 
to consider them in setting up the magnetostrictive 
equations. It can be shown that eddy-current losses 
can be taken into account by multiplying the per¬ 
meability n by a complex eddy-current factor x- 
This factor depends on the geometry of the magneto¬ 
strictive material and on a characteristic length. 



where p* = resistivity in ohm-centimeter, 
p = magnetic permeability, 

/ = frequency of applied field. 


The physical significance of d is that a magnetic 
field, applied tangentially to a thick sheet, is reduced 
to times its value at the surface in penetrating 
through a depth d. It is the same characteristic 
length which occurs in the general theory of penetra¬ 
tion of an electromagnetic wave into a conducting 
metlium (see glossary for definitions). 

For a large flat .sheet of thickne.ss t or a stack of 
such flat laminations insulated from one another, 
the eddy-current factor x depends on the ratio d/t. 
It is convenient to introduce a characteristic fre¬ 
quency fc defined by 


or 


d__ ]/2f, 
t f 


fc = 


loy 

27r“pt“ 


( 2 ) 


The eddy-current factor x can now be shown to be 


X = XoC = Xr - jxi 



(3) 


Graphs of the magnitude xo aiid the phase f, as well 
as the real and imaginary parts xr and xi of x» are 
shown in Figure 1. They can be used for curved 
sheets, where the magnetic field lies parallel to the 
sheets, provided the radius of curvature is large com- 
l^ared to d and provided the sheet does not form a 
closed electric loop, linked with the magnetic field. 
The field and current distril)utions in a sheet are 
shown in Figure 2 for the case///„ = 2.5 {t/d = 0.36). 

From equation (3) the relations 



/y 

/,./ 2835\/,,/ ’ 

17//V 


315\/, 


(d) 


apply at low frequencies and 


Xr X/ ^-f ^ -1.5° (5) 

i/| 

is valid when the fre([uency is sufficiently high. 

The eddy-current factor x can be used to determine 
the core impedance of a coil with laminated core of 
magnetic material. The core impedance is that part 
of the total impedance re.sidting from the magnetic 
flux that traverses the core which is as.sumed to have 
no gap. The total impedance consists of the core 
impedance plus the leakage impedance, the latter 
being composed of the copper resistance and the 
leakage reactance arising from the flux which links 
the winding without entering the core. Obviously, 
the splitting of the total flux into two mutually e.x- 
clusive parts, one of which lies completely in the 
core and the other completely outside the core, is 
(piite arbitrary. It is, however, a very convenient 
simplification and does not introduce serious error 
in well-designed magnetic circuits. 

If the core inductance, calculated without taking 
account of eddy currents, is Lo, then the actual core 
impedance is given by 


Zc = Re + jXc = jeoLox- (b) 


3.S 


CONFIDENTIAL 




36 


MAGNETOSTRICTIVE VIBRATORS AND EQUIVALENT CIRCUITS 



Figure 1. Eddy-cun-ent factors for flat lamina. 


© 

© 

© 

© 

© 

© 

© 

© 

© 

© 

0 


0 — 
© — 
© — 
© — 

© 

-© 

— © 
— © 
— © 
— © 


Figure 2. Field and current distribution in a plane 
sheet with f/fc = 2.5. The encircled arrows show the 
lag in pha.se. H and / are mutually perpendicular. 



Figure 3. Theoretical impedance of core composed 
of flat laminations. 


The dependence of equation (6) on frecpiency is 
shown in Figure 3, where xitf/fc = is 

plotted against xif/fc = Rc/^irfcLo, with f/fc as a 


parameter. When the frequency is low, the locus 
follows a circle with radius 1.5. In this region, the 
frequency scale along the curve can he easily found. 


CONFIDENTIAL 






























































































































KDDV ClIRRENTS 


.•{7 


since lines drawn from the point 2.5 times the 
radius) on the horizontal axis through points on the 
curve produce intercepts on the vertical axis eciual 
to the values of f/fc on the curve. The frequency 
.scale in this construction is therefore linear on the 
^'ertical axis. This is u.seful in frequency interpola¬ 
tion on an experimental curve. This rule is only 
approximate, but the error in frecpiency is less than 
1 per cent up to f/fc = 2.5 and less than 5 per cent 
if f/fc is less than 4.0. 



Figure 4. .Viiproximalc represeiitatioii of core im- 

Iiedaiice. 

At low frecpiencies, the core impedance (6) can 
be represented by the circuit .shown in Figure 4, con¬ 
sisting of the inductance Ln in jjarallel with a constant 
resistance tSirLnfc. The impedance of this circuit 
divided by the factor 2irfcLo is the .semicircle in 
Figure 3. The approximation is quite accurate up 
to / = fc, but beyond this point there are increasing 
deviations, particularh' in the resistance. 

The characteristic frecpiency/c which was defined 
in eciuation (2) gives a rough indication of eddy- 
current losses, which are large when the actual fre- 
(piency / is greater than fc but small otherwi.se. In 
most of the magnetostrictive tran.sducers which 
have lieen designed foi’ high efficiency, f/fc has been 
keijt less than unity through the operating range. 
Graphs of the characteiistic frequency in terms of 
thickness of the sheet are shown in Figure 5 for 
nickel and 2V-Permendur. These are included only 
as a guide, since other factors in equation (2) 
depend on conditions of polarization and anneal. 
The constants a.s.sumed in Figure 5 are pc = 8 X 10“'’ 
ohm-cm, p = 30 for nickel, and pc = 35 X 10“'’, 
p = 50 for 2\"-Permendur. 

When the magnetic .sheet does form a closed elec¬ 
tric loop, linking the magnetic field, eipiation (3) 
must be modifietl. This would be necessary, for 
examjile, if the sheet were in the form of a tube with 
its axis parallel to the magnetic field. Then eddy cur¬ 
rents flow around the circumference of the tube ami 
shield the interior from the applied magnetic field. 


The magnetic field can be visualized as penetrating 
from only one side of the sheet (the outside of the 
tube), whereas in a flat sheet the field penetrates 
from both sides. The situation is illustrated in 
Figure 6 in which the field and current distributions 
are shown for a closed cylindrical sheet. This figure 



I 1.5 2 3 4 5 7 10 15 20 

THICKNESS OF SHEET (MILS) 


Figure 5. Kcidy-currenl pnrainetcr fc for nickel and 
2V'-Penncndnr. 

is drawn for the same parameters as Figure 2. The 
lower edge of the sheet in the figure represents the 
inside of the cylindrical loop or tube, and the shield¬ 
ing of the insitle by the circulating currents is illus¬ 
trated b}' the decreasing field and current density. 


CONFIDENTIAL 






























































38 


IMACNETOSTRICTIVE VIBRATORS AND EQUIVALENT CIRCUITS 


©- 

©-- 

0 

0 - 
0- 
0 - 
0 - 
0 - 
0- 
0- 


e — 
© — 
0 — 
0 — 
0 — 
0 — 
© - 
© - 
© - 
0- 
0* 


Figure 6. Field and current distributions in a cylin¬ 
drical sheet with//© = ‘2.o. The field is parallel to the 
axis of the cylinder, which has a large radius in com¬ 
parison with (1. 


The eddy-current factor in this case is given Ity 

hj 

fr 


(>-©;//..siuh l/- 


X = 


;jf 

fc 


(7) 


and is plotted in Figure 7. 


It should be noticed that //, //„ B, s, and P are total 
(luantities. In general, interest will be centered on 
small changes in these tiuantities. For example, ac¬ 
cording to equations (9), the stress jtroduced by 
induction B when the strain is zero varies as the 
square of B. It is therefore customary to a])ply a 
static polarizing induction Bq and superpose on this 
an incremental induction, which for our purposes 
will vary sinusoidally with the time. The incre¬ 
mental eciuations are obtained from equation (9) 
by differentiation. By now using the same letters for 
incremental quantities which previou.sly stood for 
total (quantities. 


where 


p = -X// + Es, 
He = 11- dirX.s, 

X = 2tBa 


( 10 ) 

( 11 ) 

( 12 ) 


is the u.sual magnetostrictive constant. As shown 
explicitly bv ecquation (12) it has been a.ssumed in 
equation (8) that X is proportional to the polarizing 
induction ©o- Evidence verifying this point for 
nickel within the accuracy of experiment will be 
liresented later. 

Since now B and H (incremental values) are pre¬ 
sumed small, 

B = ixH 


3.2 THEORY OF MAGNETOSTRICTION 


Suppose that the total magnetic and mechanical 
potential energy associated with unit \'olume of the 
magnetostrictive material can be written in the form 

”■ = -'''"+f ■ 

where IF = potential energy per unit \-olume, 

H = (total) magnetic field, 

B = (total) magnetic induction, 

R = longitudinal strain (//, B, s in same di¬ 
rection), 

€ = magnetosti-icti(’e coefficient, 

E = Young’s modulus for unmagnetized ma¬ 
terial. 


The longitudinal stress P and the externallv ajrjilied 
field He are given lyy the partial derivatives 



— e/i" -)- Es, 


H — SweBs. 


(9) 


ma>' lie taken as applying in the static case and 

B = MX// (13) 

when eddy currents are present. Here m i^ the incre¬ 
mental permeability at the induction Bq. FT.se of 
equations (11) and (13) allows equation (10) to be 
rewritten 

P = —\lJixHe + (E — 47rX'’Mx)s. (14) 

The value of Young’s modulus, when the flux 
density is held constant, is E, as in equation (10); 
its value in a constant applied field, according to 
ecquation (14), is 

E' = {E — 47rX-Mx) = •£'(1 — B'x), (lo) 

where h = E is the electromechanical cou¬ 

pling. Since, as stated in equation (12), X is zero 
when the polarizing flux is zero, (1.5) can be 
interpreted as the ^'alue of Young’s modulus with 
polarizing flux, whereas its value without polarization 
is simjily E. Maximum ^'alues of k for nickel are 
of order 0.2 to 0.3, depending upon heat treatment 
and polarization. 


CONFIDENTIAL 












RADIAL viRKATiON OF ma(;nktostrh:tive RIN(; 


.{9 



3.3 RADIAL MBRATION OF MAGNETO- 

STRICTIVE RING 

♦ 

Theoretically the simplest type of magnetostric- 
ti\’e transducer consists of a core of magnetostrictive 
material in the form of a cylindrical shell. The coil 
is wound toi'oidally about this core. Two types of 
con.'^truction are shown in Figure 8. 

3.3.1 -Mechanical Impedance of Rin^ 

The impedances of this transducer are readily ob¬ 
tained. Let F be the scalar ])rcs.sure integrated over 
the cylindrical .surface. C'onsider the motion in 
which all parts of the surface have the same radial 
component of velocity. The mechanical imjjedance is 

Z,n = Rm + iA'm = R,n -(1(5) 

where -1/ is the mass of the cylindrical shell and K is 
its stiffness. The rea.son for the double jjrimes on the 
resistive component on the right will become evident 
in a moment. The mass M is 

M = 2wablpm, (l(5a) 

where p„, is the density of the magnetostrictive core 
material and the dimensions a, b, and I are shown in 



B. Core consisting of a thin-walled tube. 


C'ONFIDENTIAL 





































































































to 


MAGNETOSTRICTIVK VIBRATORS AND EQUIVALENT CIRUUITS 


Figure 8. If the core were not magnetostrictive, the 
stiffness couUl properly be written as 


2ME 

Ao = -’ 

a 


(17) 


where E is the Young’s modulus of the material. 
However, it has just been shown in equation (15) 
that even under static conditions a magnetostricti\'e 
core has a Young’s modulus E or E', according as 
the induction B or the applied field IE is held con¬ 
stant. Further, E' depends on the permeability g, 
which in the dynamic problem must be replaced by 
MX where x is the eddy-current factor. Thus E' 
depends on the frecpiency, because of eddy currents, 
and is complex, since x has an imaginary part. This 
means that the term K/joi in equation (16) is not 
purely imaginary aiui therefore represents resistance 
as well as reactance when magnetostriction is 
present. 

The i)re.sence of an additional resistive part of the 
mechanical impedance due to magnetostriction and 
eddy currents can be understood rather easily. C’on- 
sider the dissipation of power when a sinusoidal force 
is applied to the magnetostrictive core. First, of 
course, the velocity v produced by the force cau.ses 
power loss on account of the purely mechanical 
re.sistance present. Second, the velocity, being at¬ 
tended by an alternating strain, .sets up an alter¬ 
nating field through the inverse magnetostrictive 
(Mllari) effect. The magnetic field and the asso¬ 
ciated induction then produce eddy cvirrents which 
dissipate power because of the electric resistivity of 
the core. Thus there must be an additional me¬ 
chanical resistance R,'n such that the second dissi¬ 
pation of 1 ) 0 wer is R^v-. C’learly R^ depends on 
the magnetostrictive constant X or the coefficient of 
coupling k and is zero when X aiul k are made zero by 
removing the polarizing flux. The total resistance 
R„, is the sum of the two resistances A,), and A". 

Returning to the stiffness of the cylindrical shell, 
magnetostriction can be included in eciuation (17) 
by replacement of E by E' as given by eciuation 
(15). This also takes account of eddy currents 
through the eddy-current factor x, giving an effective 
permeability mx in eciuation (15). Here 


A = Ao(l - k-^x), (18) 


where A and A'o are the stiffnesses with and without 
magnetostriction respectively; k is the coefficient of 
electromechanical coupling; and x is the eddy- 


current factor. The mechanical impedance given 
in eciuation (16) can now be split into two parts, 

z„, = z; + z;,;, (i9) 

of which the second is of purely mechanical origin 
and is given by 

= a;,; + jx- = 1C + - ^). (20) 

while the first, resulting from the electromechanical 
coupling of the core material, is given by 

= A„i -b jA',„ = +ix«)- (21) 


:5..3.2 Electric Impedance of Rinj; 


The blocked electric impedance of the transducer 
can be considered in two parts. The fii'st, Z^, called 
the core impedance, is due to the magnetic flux in 
the core material. It consists of resistance as well as 
reactance, because of eddy-current losses, and has 
already been di.scus.sed at the beginning of this chap¬ 
ter. The .second, denoted Z;, consists of the re¬ 
sistance of the winding and the reactance due to the 
flux that does not pass through the core. In the 
simple cylindrical transducer, the core flux and the 
leakage flux are distinct. The core impedance is 




jco2N-bliix 

= = jwLox = - 

a 


( 22 ) 


in electromagnetic units. Here N is the number of 
turns linking the core of length I, radius a, and thick- 
ne.ss h, as shown in Pfigure 8. lAiuation (22) has 
the same form as ecpiation (6) and its dei)endence 
on frequency is shown in Figure 3. The total blocked 
electric impedance is 

Ze = Z, + Z,. (23) 


3..3..3 IVIiitual Impedance of Ring 

The mutual impedances Zem and Zmt remain to be 
determined. In this first example, particular at¬ 
tention will be given all signs and directions in order 
to .show that Zme = —Zem- Ordinarily this relation 
would be assumed. The actual .sign of Zf„., as dis¬ 
tinct from relative signs of Z^^ and Z,,,^, rarel,v is of 
much conseciuence, since it dei)ends on conventions 
cho.sen for directions of current and velocity, which 
are u.sually not specified. It should be noted that 
imi)ortant formulas like equations (20), (21), (24), 
and (25) of Chapter 2 are not affected by reversing 
the signs of Z,^ and Z,„e = — Z„„. 


CONFIDENTIAL 





RADIAL YIRKATION OF MACNKTOSTRICTIVE KING 


II 


To consider Z,,,* first, according to equation (14) 
of Chapter 2, 

(24) 

where t; = 0 in the evaluation of the ratio of force to 
current. The conventions adopted here as to signs 
and directions can l:)e made clear with the help of 
Figure 9. The positive direction of the (incremen¬ 




Figdre 9. Force produced by blocked transducer ex¬ 
cited with current 7. 


tal) induction B is the same as the polarizing induc¬ 
tion Bo in the core. This also fixes the positive 
direction of current if positive I is taken to pro¬ 
duce positive B. Positive E is then determined as 
shown by the previous convention that E/I should 
have a positive real part when the transducer is 
passive. Finally, a radially outward force over the 
cylindrical surface applied on the transducer and an 
outwardly directed radial velocity will be called 
positive. Suppose now that a positive current, in 
the direction shown in Figure 9, is passed through 
the winding. There is then an induction 

„ 2A^mx/ 

li = - 

a 

through the core in the direction shown and by the 
convention as.sumed here this is po.sitive. Since 
the tran.sducer is blocked (p = 0), s = 0 in equation 
(10), and the circumferential stress .set up in the core 
may be written 

p = -\B = - 

a 


The corresponding total radial force Is 


F = 2irbIP 


— -iirXNblfjLxI 
a 


It should be noted that P is negative (compre.ssion) 
and that F is also negative (radially inward). Finally, 
from eejuation (24), 


(’onsider now the other mutual impedance, 



The surface of the transducer is set in motion with 
velocity v. The strain, which is proportional to the 
integrated velocity, is 

V 

joja 


Since / = 0, there is no externally applied magnetic 
field (disregarding static polarizing fields) and equa¬ 
tion (11) gives 


II = dirXs 


47rXl> 

joia 


for the magnetic field produced by the motion. The 
direction of this field is shown in Figure 10. The 
flux in the core as a result of the field H is 


4> = 


47rX6^X*^ 

-, 

jua 


and the generated open-circuit voltage 

r 4ir\Nblnxv 

E = A — = juN4> =-’ 

dt a 

where the direction of E is shown in Figure 10. 


(27) 



Figure 10. Open-circuit voltage jiroduced by trans¬ 
ducer driven with velocity v. 


Compari.son of eipiations (26) and (27) allows the 
conclusion 


Z 


em 


•iTrXNbliix 

a 


(28) 


CONFIDENTIAL 


































42 


MA(;NKT0STRICT1VK VIBKATOKS and EgriVM.KNT CIKCLIITS 


Thus the mutual impedances as given by ecpiations 
(25) anti (28) are etjual in magnitude but opposite in 
sign, in accord with equation (17) of Chapter 2. 


3.3.4 Relation Between Z,'„ and Z,. 

Some relation might reasonably be expected l)e- 
tween the part Z,', of the mechanical impedance and 
the core impedance Ze, involving also the mutual 
impedance This follows, since Z'„^ is, in a 

manner of speaking, the reflection of the core imped¬ 
ance in the mechanical .system. From equations 
(21), (22), and (28), it can ea.sily be found that 

^ ( 29 ) 

liquations for the four-terminal, electromechanical 
network may be written, therefore, as 

E = {Zi + Z,)I + Z,^v, 

\ X (30) 

F= -z,j + [z:, ~-£‘y 

where Zi is the leakage (and copper) impedance, Zc 
is the core impedance given l)y equation (22), Z^^ 
is the mutual impedance given by ecpiation (28), 
and Z” is the mechanical impedance in the absence 
of magnetostrictive coui)ling, represented by equa¬ 
tion (20). 


this concerns the term — in the mechanical 

impedance. An analogous term Zf,n Z^ in ecpiation 
(45) of Chapter 2 provided a ba.sis for representing 
these ecpiations by the L section (and transformer) 
of Figure 10 of Chapter 2. In general, a T section 
would have been required. Here too, through use 
of the term — Z(,^/Zc, the number of elements re- 
(piired in the e(iui\'alent circuit can be reduced by 
one. 

A voltage c and a currtmt i are introduced through 
the relations 

F = jc, V = ji, (31) 

which imply that e and i are 90 degrees out of pha.se 
with F and v respectively. Ec(uations (30) become 

F = (Z, + Z.)/-hiZ.„,f, 

e = jz.j -f (^z;,; - 

Since the new mutual impedances are both jZrm 
with no difference of sign, equation (32) can be 
represented formally by an equivalent electric circuit. 



I I0<{)^ 



Z“ 




I = v/i 


t 

F/j 

—o 


Figure 11. Kquivaleiit circuit for cyliiulriciil niag- 
iicto.'st rict ive t rant^ducer. 


3.3.5 Equivalent Electric Circuits 
for Rin^ 

It has been stated previously that an equit-alent 
circuit is unobtainable for an electromechanical trans¬ 
ducer of the electromagnetic or magnetostrictive type 
when forces are replaced by voltages and velocities by 
currents. The reason for this is that these two types 
of coupling lead to mutual impedances equal but 
opposite in sign, while purely' electric circuits al¬ 
ways lead to the same sign. In the dynamic speaker, 
this difficulty was avoided by replacement of forces 
by currents and velocities bj^ voltages, since then the 
cross coefficients [equation (45) in Cliaiiter 2] had 
the same sign and could be reijresentetl as mutual 
impedances in an ecjuivalent electric circuit. Al¬ 
though the .same process can l^e carried through 
for magnetostrictive transducers,it is more con¬ 
venient to use a different approach. The reason for 

“ This is the method u.sed by Mason.*® lie h.a.s omitted 
losses due to eddy currents in his treatment. 


This circuit is shown in Figure 11, where the tfan.s- 
former is ideal and has the impedance ratio <h- 
= {jZem/Zc-)- in the direction indicated. From 
equations (22) and (28) for the cjdindrical tran.sducer. 


as the turns ratio of the ideal transformer. Here N 
is the number of turns on the core,/is the fretiuency, 


Z'4 



and X the magnetostrictive constant. The fact that 
the turns ratio is dependent on frequency is unortho¬ 
dox here, but it introduces no formal difficulty. By 


C’ONFIDENTIAL 






















KVDI VL MHRATION OF M V(;NKTOSrKI(;TIVE KINO 




use of the forms already found for Z;, Z^, and Z”, 
the more explieit etiuivalent circuit shown in Fig:ure 
12 is obtained. The parallel representation for Z^ 
has already been discussed (Section 3.1). 


.3..3.6 


Efficieiicv of Kiiij; 


Some additional information can be extracted 
from ecpiations (29) and (33). With these ecpiations 
rewritten, 


inary parts. 


Zm 

■ (f) 

fz,. 

jZem 

X 


Zc 



ns are 

split into their 

Rin 

X,;, / 


Rc 

XL \ 

,Xf/ ’ 


-Rc 

A/. 

R cm 

" AL,„ “ 

X ’ 


The.se can be combined to give 

itx,: = 

= XL,. 


(34) 


Consider eciuation (21) of Chapter 2 the general 
formula for efficiency obtained previously. If it is 
a.ssumed that leakage inductance and cojiper resist¬ 
ance are negligible so that Z^ = Zc, this equation 
can be written 

, .-</C + .V;„,) _ 

AB + C 

where A = Rc (R,,, + Rl) + Rim . 

B = Rc {Rm A- R l) - XL , 

C = [/fr (-T,„ -|- A /,) -|- RcmXcm]’ ■ 

Rememl)er that R,„ = Ri,, -|- Rm Xm = 

Xn + X;L where the double-primed (piantities 
are of purely mechanical origin and the single-primed 
are reflections of the core impedance into the me¬ 
chanical system by the magnetostrictive cou])ling. 
Then ecpiations (34) can be used to eliminate 
and X',), from equation (3o), with the result: 

Rl (Rim + A'bJ 


DF + G 

where 1) = Rc {R'm + Rl) + Rem + Xi,,, , 
F = R',: + Rl, 

G = Rc (X'„, -f- A'/,)". 


3.3.7 Frequencies of Maximum 
Effieieney and Resonance 

It has previously been shown in eciuation (22) 
of Chapter 2 that maximum efficiency, with respect 
to X L, occurs when the sciuared bracket in the de¬ 
nominator of eciuation (35) is zero (according to eciua¬ 
tion (30), when X),) -|- X'/, = 0). If freciuency is con¬ 
sidered the variable instead of A'/., it is still true that 
maximum efficiency occurs for A'”, A"/, = 0 pro¬ 

vided, as is usually the case, that a variation of fac¬ 
tors other than A'" -T X l can 1)C neglected. On the 
othei- hand, resonance occurs when the total me¬ 
chanical reactance is zero. Denoting by fg and fg 
the freciuencies of maximum efficiency and resonance, 
respectively, 

x;,: + Xi = 0 at/«, 

XL + A )„ X = 0 at/ii. 

Note that/i' is constant, independent of the magneto¬ 
strictive coupling, whereas/fi is variable, depending 
on this couijling. If the magnetostrictive coupling 
is small, A",'„ is small and//; approaches/s. In other 
words, fg is the value of fg without coupling. As the 
coupling is increased, A',), increases and fg is de¬ 
pressed below fg. Later in this chapter it will be 
shown that this relation can be expressed in terms 
of an effective coupling coefficient k\.(f by 

fg 

h 

At fg, the fiequency of maximum efficiency, etiua- 
tion (36), reduces to 

1 Rl 

(37) 


= y/\ - Ft 


Fff,„nv = 


1 + 


Rc{Rm + Rl) R'm + Rl 
R'em + A’L 


For the cylindrical transducer, equation (37) can 
be simj^lified by the use of forms that have been 
found for the various impedances. Bj' substituting 
equations (22) and (28) into (37), 

1 Rl 


Fff„.,v = 


1 + 


fsaxiiRm + A/,) 


Rm A- Rl 


(38) 


(36) 


AwX-bRxo 

where fg = frecpiency of maximum efficiency, 
a, b, I = dimensions as shown in Figure 8, 

Xi, Xo = eddy-current factors (Section 3.1), 
g = permeability, 

X = magnetostrictive constant, 

/f” = internal mechanical resistance of purely 
mechanical origin, 

Rl = mechanical load resistance. 


CONFIDENTIAL 














MAGNETOSTKICTIVE VIBRATORS AND EQUIVALENT CIRCUITS 


U 


3.4 LONGITUDINAL VIBRATIONS 

The masnetostrictive I’od in longitudinal vibration 
is essentially more comjjlex than the cylinder or ring 
just considered. At any instant, different jwints 
in the rod have different velocities and different 
stresses, in contrast to the ring, where ratlial veloci¬ 
ties and longitudinal stresses are the same for all 
))arts of the ring. This is another way of .saying that 
the ring is a lumped system but the rod is a distrib¬ 
uted system. 


3.4.1 Rod as a Six-Terminal 
Network 

If forces are allowed to act at both ends of the rod 
(or tube) .shown in Figure 13 the system can be 
considered to have two pairs of mechanical terminals 
and one pair of electric terminals. Po.sitive direc- 


• X -► 


- 

>4 


- 1 - 

I 


6- E -► 6 


Figure 13. M.ngnetostrictive rod in longitudinal 
vibration. 


tions of the velocities and the forces applied to the 
rod are shown. A polarizing induction Bq is .supposed 
to exist in the direction which corresponds to positive 
incremental induction B and to positive voltage and 
current. Distance from the left end of the rod is 
mea.sured by the variable x, and the displacement 
of the point with equilibrium position at x is ^(x, /) 
measured to the right. Thus the values of x at the 
left and light ends, (1) and (2) in Figure 13, are 
respectively x = 0 and x = 1. Also 

*^1 = —^x = Q< = G = /, 

Avhere the dot denotes a partial differentiation with 
respect to time. The rod will be taken to be long 
and thin, so the demagnetization can be ignored. 
The induction B is then gi^’en by B = nxH, where 
11 is the average field along the rod, produced by 


current in the winding and by strain in the rod. 
According to equation (11), 

// = He + dirXs, 

where He i;^ due to the current, s is the strain, and X 
is the magnetostrictive constant. In terms of the 
variable the average strain is 
. _ ^2 - 
^ / 

.SO that the induction B can be written 
B = Be -\- 47rXMX«, 

47rX^ix(^2 — ^i) 


(39) 


= MX^/ * + 


I 


The stre.ss P in the rod is found from equation 
(10), thus, 

jP = — \B -)- Es, 

in which E is Young’s modulus. With the help of 
equation (39), 


P = -\Be - 


47rXVx(^2 — ^i) 


+ E 




(40) 


I ' dx 

is evolved, in which dx has been written for the 
strain s. The equation of motion is then simply 


dx dx- 


(41) 


since the first two terms in eipiation (40) do not 
depend on x. The solution of equation (41) is u.sed 
in the form 

^ = c^“'(Ci cos kx Co sin kx), (42) 

in which k = (j}\^p„JE = u/cm is the wave number 
when the iiuluction is held constant, or when the 
magnetostrictive constant is zero. 

44ie boundary conditions remain to be defined. 
The.se are 


P = 


Vi at X = 0, 


Fo 


m 


P = —, ^ = Vo at X = Z, 


where a is the cro.ss section of the rod. 

Equations (40) to (43), with a little manipula¬ 
tion, yield 

ATvX-apxii’i + rO 


F, 


■ XaB. 


jul 


— j{pca)m{v\ cotan kl vo co.sec kl), 


Fo = — \(tB, — 


■iirX-ffpxjVi + Vi) 
jul 


(44) 


— j{pc(x)m{vi cosec kl + Vo cotan kl). 


CONFIDENTIAL 























LONGITHDINAF. VIBRATIONS 


15 


The induction B, due to the externally api)lied field 
is 



It is convenient to let 


G 


AirXcrNux 


(45) 


so that the terms 'KaBe in equations (44) are ex- 
])ressed merely as GI. By neglecting demagnetiza¬ 
tion, the core impedance can be written 


(4U) 

Then the voltage across the winding is found with the 
aid of ecpiations (39) and (43): t 

7^.. /V ^ 1k 

E = Zil ^ NaB 

= {Zi +Z,)I+ Gv, + Gv^, 

where Zi represents copper resistance and leakage 
inductance. Eciuations (44) can be rewritten with 
the abbreviations (45) and (46) 


El = 


— — ^jipcar 


s ,, G- 

)m cotan kl + — 


Vl 


j{pC(T)m co.sec kl -f 


ft 


(48) 


F, = -GI - 


j{pc<T)m cosec kl + 


CP 


j{pca)m cotan kl + 


a- 


Equations (47) and (48) are the final results for 
the magnetostrictive rod as a six-terminal network. 
Notice that the mutual impedances G appear with 
opposite signs. Later the system will be reduced to 
a four-terminal network by appropriately termi¬ 
nating one end of the rod. 


3.4.2 Six-Terminal Equivalent 
Networks for Rod 

Ecjuivalent electric circuits^for the rod can be ob¬ 
tained by the same methods as were used previously 
for the ring. Let 

Ey jC\, F 2 ( 49 ) 

Vl = jil, Vi = jii. 

Ecjuations (47) and (48) become 


E = (Zi + Z.)I -P jGii + jGii, 


ei = jCrl - 


Ci = jGI - 


jipc(x)„ cotan kl 


(50) 


- j^i(pca)„. cosec kl + 


j{pca)m co.sec kl -f- 


(72 


Z,J 

jipcajm cotan kl + — h' 2 . 


These equations are .satisfied by the voltages and 
currents of the networks shown in Figures 14 to 16. 



Smooth line with length propagation velocity ond 
iterative impedance (pc 0 *)^^ 



Figure 14. Equivalent circuit for magnetostrictive 
rod. 



Figure 1.5. Equivalent T circuit for magnetostrictive 
rod. I 



Figure 16. Equivalent w circuit for magnetostrictive 
rod. 


Note that the ideal transformer here has a turns 
ratio differing by a factor of 27r from that found for 
the ring. For any narrow range of frequency, the 
equivalent circuit can be simplified by introducing 
lumped constants to replace the smooth line. The 


CONFIDENTIAL 




















































46 


MA(;.\Kr()STKICTIVK VIBRATORS AND E(>UIVALFaNT CIRCUITS 


error made in doing this is small if the freciuency 
range over which it is used is small. For example, 
when the rod is close to half a wave in length, the 
circuit is as shown in Figure 17. Here the induct- 



Figure 17. Equivalent lumped circuit for half-wave 
magnetostrictive rod. 


ances and condensers in the mechanical part of the 
circuit have been marked with their values in terms 
of the mass of the rod 3/ = lapm and its static stiff¬ 
ness A'o = Ea I (E = Young’s modulus) without 
magnetostrictive coupling. The ideal transformer 
marked (p = —I takes account of the jihase in¬ 
version jiroduced by a half-wave transmission line. 
(The black dots indicate corresponding ends of the 
two windings.) 


3.4.3 Rod with One End Free; 

Equivalent Cirenits 

The equivalent circuit for a rod which is free on 
one end can be obtained by shorting that end 
(Figure 15). The re.sult is shown in Figure 18, in 
which the .subscripts on the mechanical voltages and 



Figure Equivalent^ circuit for magnetostrictive 
rod free on one end. 


currents have been dropped, since the system has now 
reduced to a four-terminal network. The circuit 
can be put in more useful form by transforming the 
T network of mechanical elements into an L network 
with the help of the eiiuivalence shown in Figure 19. 


In the present case, .1 and B are eipial, so that the 
impedance ratio of the transformer in Figure 19 is 
1 to 4. After use of Figure 19 the two .series-arm 
impedances can be combined and the circuit shown 
in Figure 20 results. 



I to [(A+B)/0]^ 



Figure 1!). Equivalence used in transforming tin 
circuit of Figure IS into the L circuit of Figure 20. 



/ 



As before in Figure 17, the mechanical impedances 
can be rejire.sented by lumjied inductances and 
capacities if the frecpiency range is restricted. If 
the frequency is near /j = Cm/2/, which makes the 
rod half a wa\'e in length, the series ai'in is accurately 
represented by a resonant circuit and the shunt arm 
by an antiresonant circuit. The frecpiencies of 
resonance and antire.sonance are both /p The cir¬ 
cuit constants are shown in Figure 21 in which 3/ 



Figure 21. Equivalent circuit for half-wave mag- 
uetostrictivp rod free on one end. 


is the mass of the rod and Ko in the static stiffne.ss 
without magnetostrictive coupling. At /i both the 
magnitude and the frecpiency dependence of the 
two mechanical arms are (“orrect. 

The circuit shown in Figure 22 gives the correct 
impedances at/i, where the rod is a cpiarter wave in 
length. This circuit does not give cjuite the right 
variation of the reactances with frequency since it 
has only one com]ionent in each arm. It is .suffi¬ 
ciently accurate for many purpo.ses, however, and 


O'ONFIDENTIAL 


“Vj 


































































LONGITUDINAL VIBRATIONS 


17 


has the advantafi;e of simplicity. If necessary, more By starting either from Figure 18 or Figure 20, it 
complicated circuits can be drawn or Figure 20 can is found that the circuit of Figure 24 results. Here 
be consulted. Both Figures 21 and 22 show the 



Figure 22. p]qui\'alent circuit for quarter-wave mag- 
netostrictive rod free on one end. 



I TO't' 






3|-j{/Dca)m colon K-^|^ 




I i(/°cp')m ton k-e | - ^kcML[ 
e = F/j 


({i=i G/Zc --X/N(j 


(J) = I - sec k£ 


Figure 24. I'.quivalent circuit for inagnetostrictive 
rod witti load consisting of series mass and resistance. 


core impedance as a fixed inductance and the re¬ 
sistance in parallel, in accordance with the approxi¬ 
mation discu.ssed in this chapter in the .section on 
eddy-current theory. 

.3.4.4 Kod with One End Free and 
the Other Loaded with IMass and 
Resistance 

One type of inagnetostrictive transducer consists 
of a heavy steel plate with longitudinally vibrating 
nickel tubes mounted on one side. The other side of 
the plate is in contact with the water and is thus 
loaded with the radiation impedance of the water. 
Usually this impedance is a jnire resistance equal to 
the specific resistance pc per unit area over the 
frequency range of the device. The principal effect 
of the plate is to introduce a mass in series with 
the radiation resistance as the load on the indi¬ 
vidual tube. 

In order to examine this situation it is convenient 
to make a transformation of the equivalent circuit 



Figure 23. l^quivalence used in transforming Figure 
18 into Figure 24. 


shown in Figure In Figure 20, by means ol the 
ecpiivalence of Figure 19, a circuit was obtained in 
which the mechanical elements were represented by 
an L section with the open end of the L facing the 
electric terminals. The transformation will now be 
made in such a way that the L faces in the opposite 
direction. For this the equivalence given in Pdg- 
ure 23 is required. 


the mechanical load consisting of joiM l — jkcMi 
in series with El has been shown. The equivalent 
circuit to the left of the mechanical terminals is 
correct no matter what the mechanical termination. 
It will be noticed that the second transformer has a 
turns ratio which depends on frequency. In 
fact, when the rod approaches a quarter wave in 
length, F' liecomes indefinitely large. In actuality 
this circuit is useful only over a narrow range, 
sufficiently removed from the frequency of cpiarter 
wave length so that can be regarded as constant. 
The frequency range of consequence lies about the 
point where the series mechanical elements j{pca)m 
tan kl and jkcM l are resonant. This is the resonance 
of the mechanical system when the inagnetostrictive 
coupling is zero. Also, if the leakage impedance is 
small, as assumed previously for the ring, it is the 
frequency of maximum efficiency which was denoted 
by/ff. Here a subscript 0 will be u.sed to designate 
this frequency in order not to compromise Z;. 
Whenever Zi is sufficiently small, /o can be identified 
with/fi. Look first at the circuit for the one frequency 
/o and ignore for the moment what happens in its 
vicinity. As stated, the reactance of the series 
mechanical arm becomes zero. This condition may 
be written as 



where ko = 27r/o/c„, is the wave numlier at frequency 
/o, and niQ = {pa)m/kn is the mass of a section of the 
tube l/27r times a wave length (one radian). Also 
the .shunt element is 


—j(pca)m cotan kol = j{pca),„ 


nio 

dir' 


The turns ratio «!>' is given by 


= 1 — sec k,tl = 1 



CONFIDENTIAL 



































18 


IVIAGNETOSTRICTIVE VIBRATORS AND EQUIVALENT CIRCUITS 


Ri, since they increase the total current. If the 
efficiency Is to be higli, it is necessary for the trans¬ 
formed load resistance to be low compared with /v. 
Thus either the core must be well laminated, which 
raises rc, or Mi/mo must be large in order to reduce 
the transformed load. It is not feasible to increase 
Mi/mti indefinitely, since eventually the load resist¬ 
ance becomes less than the copper resistance Ri and 
also since there are always internal mechanical 
los.ses, .some of which increa.se with ML/nh] (see next 
section). However, it is po,ssible to obtain a mate¬ 
rial increase in efficiency l)y this device when the 
eddy-current losses would otherwise be exce.ssive. 

Figure 26 shows two of the important cjuantities 
connected with the circuit of Figure 25. The param¬ 
eter Ml/ mo against which the curves are drawn 
is the ratio of the mass of the plate a.s.sociated with 



0.1 0.2 0.3 0.5 1-0 2-0 4-0 6-0 10 

fTlQ 

Figure 26. 'Mechanical impedance transformation and mechanical Q for transducer of tube-and-plate coast met ion. 


sistance representing eddy-current losses and the one tube to the ma.ss of a section of tube l '27r times 
mechanical load resistance. The other two paths, of a wave in length. The impedance ratio is shown 
course, increase the losses in the copper re.sistance by the lower curve. The cpiantity actually plotted 


t\’ith the use of these eejuations, we find that Figure 
24 reduces to Figure 25 at frequency /o. The 
mechanical transformer has been removed and the 
load resistance divided by the impedance ratio 4>'“. 



Zc 

1 T( 






o o 

'’c 1 


o o 

o- 





(^c<7)mmo 


ujq Ml J 




= ) g/Zj = X/No) 


Figure 25. Equivalent circuit of Figure 24 at reso¬ 
nance of series arm. 


In Figure 25, it is .seen that current flowing into the 
transducer has four competing shunt paths. Only 
two of these are dissipative, namely, the core re- 


CONFIDENTIAL 































































GKOAIETRY OF THE IMPEDANCE DIAGRAM 


19 


is since ^' = 2 when Ml = 0 and the tube is 

a half wave in length. The upper curve gives the 
Q of the mechanical system expressed in mvdtiples 
of the Q = Qa, which obtains when the mass of the 
front plate M l is zero. Then 



Figure 26 shows that Q„, increases rajjidly as more 
mass is attached to the tube. The breadth of re¬ 
sponse which is inversely proportional to Q„, de¬ 
creases corresjiondingly. 

Until now the frecpiency has been considered as 
being held constant at/o. If the frequency is allowed 
to vary slightly in either direction from /o, the ele¬ 
ment in the circuit of Figure 24 that varies most 
rapidly is the series mechanical arm, provided that 
Qm is large. When this is assumed to be so, the 
turns ratio <!>' = 1 — sec kl may be regarded as 
constant and equal to 4>o == 1 ~ W. The shunt 
mechanical arm, too, usually has a high impedance 



L| = mo[kot sec^kp.^ ton 

l/C| = mooio^ [ko't sec^koi-ton ko^^/z 

Figure 27. Approximate equivalent circuit for mag- 
netostrictive rod with loarl consisting of .series mass 
and resistance. 


the ring de.scribed earlier. There the mechanical 
system was simple enough so that a reasonably 
accurate representation could be expected by in¬ 
sertion of a constant mechanical resistance in series 
with the mass and stiffness of the ring. Further¬ 
more, elaborate transformations of the system were 
not required in examining its behavior so that the 
addition of this resistance introduced no great 
complication. With the magnetostrictive rod, how¬ 
ever, matters are somewhat different. In Figure 14, 
series resistance may be inserted along the smooth 
transmission line to simulate frictional resistance 
opposing the velocity at points along the rod. In 
addition, lumped resistances may be added at the 
ends to represent, for example, dissipation in support¬ 
ing members. These resistances greatly complicate 
transformations in the system. They may be repre¬ 
sented apin'oximately by adding an equivalent in¬ 
ternal resistance in series with the load. It should 
be remembered, however, that such an ecpiivalent 
resistance will not, in general, be constant either with 
changes of freciuenc.y or conditions of loading. Take, 
for example, the problem just investigated of the 
mass-loaded tube of Figures 24 or 27. Resistance 
introduced anywhere except at the loaded end of 
the tube will not be transformed by the same 
mechanical tramsformer shown in Figure 24. The 
equivalent resistance, introduced in .series with the 
load, will therefore not remain constant as Mi/mn. 
is increased but will also increase. Eventually this 
increase will cause the efficiency to fall off as already 
noted. 

3.5 GEOMETRY OF THE IMPEDANCE 
DIAGRAM 


compared with other shunt paths, especially when 
M l/otq is large. Thus it will be omitted entirely, so 
that Figure 24 in the vicinity of /o can lie represented 
by the approximate circuit shown in Figure 27. 

It will be observed that Figure 27 has been reduced 
to the same form as the circuit for the simpler case 
of the ring as shown in Figure 12. 

3.4.5 Internal Mechanical Losses 

It is apparent that no allowance was made for 
internal mechanical resistances in the preceding sec¬ 
tions that treated the longitudinal A'ibrations of a rod. 
Such a resistance was included in the treatment of 


In this section some of the more important geo¬ 
metrical relations which hold in the impedance 
diagram for a magnetostrictive transducer will be 
given. Of necessity, numerous restrictions and 
approximations are made in the interests of sim¬ 
plicity. Thus the idealized im])cdance diagram to 
be discus.sed will be only an approximation of the 
actual one but will still be valuable as a guide in 
interpretation. 

The case considered explicitly will be the cylin¬ 
drical shell or ring for which the eipiivalent circuit 
was obtained in Figure 12. This is not .so great 
a specialization as it would .seem at first sight, since 
other systems can be approximately represented Iw 
the same eciuivalent circuit. The half-wave magneto- 


CONFIDENTIAL 



















MAGNETOSTKICTIVE VIBRATORS AM) EQUIVALENT CIRCUITS 


■>() 


strictive rod as sliown in Figure 21 is the same if the 
shunt antiresonant elements are omitted. If, as will 
usually be true for this system, the load resistance 
is not large, these elements will present a com- 
j)aratively high impedance, and their (^mission will 
introduce no serious error. Another case, in which 
the equivalent circuit is almost the same as for a 
ring, is the example just investigated of the mass- 
loaded tube (Figure 27). 

The core will be assumed to be composed of flat 
sheets, the flux lying in the plane of the sheets. As 
long as circulating eddy currents do not flow, the 
sheets can be curved. Thus slotted tubes are in¬ 
cluded. Eddy-current effects will be considered 
small in the sense that///c is less than 2, for instance. 
According to figure 3, the core can then l)e rei)re- 
sented as a i)arallel resistance and inductance. If 
leakage inductance and copper resistance are now 
negligible, the impedance of the transducer is the 
same as that of the circuit in Figure 28. Here the 


MECHANICAL 



Figure 28. Circuit representing loaded inipeilance 
of transducer. 


electromechanical transformer has lieen omitted by 
multiplying the mechanical elements by the proper 
imjiedance ratio 1 T'b The mechanical Q will be 
considered to be very high. Then there is a com¬ 
paratively slow change of the Idocked (core) imjied- 
ance, and the loop in the locus of the loaded 
imjtedance will be nearly a circle. Also, the vari¬ 
ation of <t> with frequency can be ignored. 

Figure 29 shows the idealized impedance diagram. 
The locus of the blocked impedance is the circular 
ai’c 00' with radius r and with center at C on the 
I'esistance axis. The lai'ge motional circle with 
diameter Da is obtained with the transducer in air, 
that is, with the load resistance in Figure 28 short- 
circuited. Resonance occurs at jioint Ha (in nir), so 
that the resonance diameter passes through C and 
meets the blocked impedance liiu' at right angles. 
Angle f who.se tangent is xi/xk ii^ the comjilement 
of the phase angle of the blocked impedance at 
resonance and also, from eciuations (53) of Chap¬ 
ter 2 and (28), is one-half the angle between the 


resonance diameter and the horizontal. Here xn, 
Xi are the eddy-current factors. 

The smaller motional circle is the motional imped¬ 
ance of the transducer in water, that is, with the load 
resistance in Figure 28. Larger or smaller circles 
can be drawn to correspond to smallei or larger 
load resistances respectively. The circle actually 
drawn represents the ojjtimum mechanical loading, 
so that the maximum efficiency, which occurs at 
jioint E, is equal to the potential efficiency. The 
o]ffimum circle may be found by the following 
geometrical construction. Draw the auxiliaiy circle 
which pas.ses through O and 0' and has its center 
on the reactance axis. This circle has radius r tan i' 
and is the locus of the jioints of maximum efficiency. 
This is most easily seen by noting that the su.scept- 



Figure 29. Idealized imiiedanee diagi-ain for ti'aus- 
ducer in .air and water. 


ance at maximum efficiency is equal to the core 
susce])tance, since the mechanical arm is resonant. 
The locus of constant susceptance is a circle passing 
through the origin and having its center on the re- 
ai'tance axis. The auxiliary circle must intersect 
the motional circle in water, whatever its size, and so 
must pa.ss through O'. To find the optimum water 
circle, ilraw the horizontal diameter of the motional 
circle in air. This diameter, incidentally, intersects 
the air circle on the line 00' at the ])oint A. Now 
the point of maximum efficiency E on the optimum 
water circle must lie on the horizontal diameter, since 
there is then a motional reactance at E eipial to one- 
half the motional reactance at Ka, in accordance with 


CONFIDENTIAL 




















MOTIONAL ADM ITTANCE 


31 


equations (63) and (65) of Chapter 2. The point E, 
therefore, lies at the intersection of the auxiliary 
circle and the horizontal diameter. The optimum 
circle in water may now be constructed, since it 
jiasses through O' and has its center on O'Ra. As 
an aid in constmction, it may be noted that the 
auxiliary circle intersects all motional circles at 
right angles. 

In Figure 29A the construction for an actual trans¬ 
ducer is carried out, using the data presented in Fig¬ 
ures 15, 16, and 17 of C'hapter 2. These were for a 
ring stack of annealed nickel laminations 0.()05-inch 


circle and the water circle corresponding to the 
frecpiency of maximum efficiency does not, as in the 
ideal case, fall upon the horizontal diameter of the 
ail- circle. This would occur only in the case of 
optimum water loading. It should be pointed out 
that the actual transducer used to illustrate the ideal 
construction is an exce])tionally fortunate choice. 
The critical frequency for 5-mil nickel is 80 kc (see 
Figure 5), so that eddy-current losses at the re.so- 
nance freipiency (about 55 kc) are small and the 
clamped impedance falls on the low-frequency por¬ 
tion of the curve of Figure 3. Further, the flux 



thick, toroidally wound and polarized by direct cur¬ 
rent. The center of the clamiietl impedance arc 00' 
was determined by the three points rei^resenting the 
impedances at 0, 30, and 80 kc. Point O' correspond¬ 
ing to the clamped impedance at 55kc (apjiroximately 
the resonance frecpiency) was fixed by interpolation 
along the arc between 30 and 80 kc. The motional- 
impedance circles of Figures 16 and 17 ot Chapter 2 
were drawn tangent to the clamiied-impedance arc 
at point O'. The center of the auxiliary circle is the 
point of intersection of the bisector of the angle 2.C 
with the reactance axis. It will be noted that the 
radius r of the clamped impedance arc pas.ses nicely 
through the center of the air circle, but not through 
the center of the water circle. This represents a 
small departure from the itlealized tran.-^ducer. 1 he 
point E which lies at the intersection of the auxiliary 


leakage in a toroidally wound ring stack with d-c 
polarization is extremely small. The slight differ¬ 
ence between the potential efficiency and the 
efficiency at resonance as computed from ecpiation 
(57) of Chapter 2 indicates that the ideal conditions 
assumed in Figure 29 ar(‘ closely ai)proximated in 
the actual case. 

Although the ideal construction will not in general 
be found to apply so well as in the foregoing example, 
fretiuently it will prove a useful tool in analyzing 
tran.sducer performance. 

.?.6 MOTIONAIv ADMITTANCE 

The impedances — self and mutual — of a trans- 
ducei', its motional impedance, and impedance dia¬ 
gram have already been examined ciuite thoroughly. 


CONFIDENTIAL 





























































o2 


>ia(;nktostri(.tive vibrators and equivalent circuits 


There are some a(.l^•antages, with respect both to 
measurement and to interpretation, which may he 
gained l)y the use of admittance instead of imped¬ 
ance. The comparison between admittance and 
impedance bridges will be found in Chapter 11. 
From the stamlpoint of interpretation, it should be 
remembered that the impedances of several series 
elements are additive, while the admittances are 
combined in more complex fashion. Thus, in the 
dynamic speaker, according to Figure 5 of Chapter 
2, there is a j^urely electi'ic imj)cdance in series with 
a group of elements of mechanical origin, repre¬ 
senting the motional impedance. Since the two are 
in .series, their imj^edances are additive and will l)e 
more easily .separated in an impedance diagram 
than an admittance diagram. Contrast with this the 
eciuivalent circuits of Figures 11 and 12 for the 
magnetostricti\'e ring. Here the two important 
impedances and Z','/<t>- are in parallel when 
viewefl from the electric terminals, the mechanical 
terminals being short-circuited. It is true that Z; 
rejn-esenting the leakage inductance and copper re¬ 
sistance is in series with the combination, l)ut in 
many ca.ses Z; will be negligibly small, as was 
assumed in Figure 28 in the di.scussion of the imped¬ 
ance diagram. If Zi is omitted, the admittances 
Yc = I 'Zc and 'h'H’” = <h- Z” are adtlitive and are 
easily .separated in the admittance diagram. When, 
as in Figure 28, the mechanical terminals are not 
.shorted but are connected to a load Z^, the atlmit- 
tance I'J,' is i-ejjlaced l)y 




(51) 


lly making u.se of eciuation (d) the core admittance 
may be written 


To = G. - jB^ = ^ 
Zc 


(52) 


where Ch and Be are the core conductance and sus- 
ceptance respectively and Lo is the core inductance at 
low fre(|uencies. Throughout this report, suscej3tance 
B will l)e taken as the negative imaginary ])art of 
the admittance. The .signs of reactance X and 
susceptance B are then the .same. In Figure 30, 


= 27rfeUBe 

/Xo" 

is plotted against 

= 2x/,LoG., 

JXo~ 


with f/fc as parameter. Pdgure 30 .shows the vari¬ 
ation of core admittance with frequency. When 
f/fc < 2, Ge is nearly constant, since Figure 30 is 
close to a vertical straight line. This straight portion 
is the geometrical inversion of the circle which the 
core impedance followed at low frequencies in 
Figure 3. 

In examining the geometry of tlie admittance 
diagram for a transducer the same restrictions are 
made as were matle for the impedance diagram. 
The e(iuivalent circuit is the .same, then, as tlait 



Figure 30. Theoretical admittance of core comiio.'ed 
of flat laminations. 


drawn in Figure 28. The admittance diagram is 
shown in Figure 31. It repre.sents the .same idealized 
transducer whose impedance was plotted pre\’iou.sly, 
since it was obtained l\y geometrical inversion of 
Figure 29. The same letters have been used to 
designate corresponding points in lioth figures. 
Note that the locus of jioints of maximum efficiency, 
which was previously the arc of a circle, is now the 
horizontal straight line O'EF. This is an important 
advantage of the use of admittance, since maximum 
efficiency is usually more important than resonance. 
Similarly, the locus of jioints of resonance, which 
was previously the .straight line ()'R\vBaC (the 


CONFIDENTIAL 






































DEDUCTIONS FROM ADMITTANCE DIAGRAM 




resonance diameter), is now the circle O'RnCRAO" 
with horizontal tangent at (Y. 

The construction of the optimum motional circle 
in water, such that the efficiency at E is the potential 
efficiency, follows the construction jjreviously used 
in Figure 29. The inversion of A EH, the horizontal 


^ * 




tff'O' 




\ I pO'N'' 

- 7 ^- 

'< /^OPTIMUM motional 
' , circle IN WATER 


LOCUS OF MAX EFF 




J^COF resonance 


Figure 31. Idealized admittance diagram of trans¬ 
ducer in air and in water. Corresponding points liave 
the same letters as in Figure 29. 


diameter of the impedance circle in air, is the arc 
AEHO". The point .4 is fixed by the intersection of 
the straight line 0"0' with the admittance circle in 
air. The arc is then determined, since its tangent at 
0" is horizontal. The arc’s intersection with O'F 
is at E, and O'E is the horizontal diameter of the 
optimum motional circle. 

The admittance of the transducer, under the 
simplifying assumptions made, has been shown to 
be the sum of two admittances 

1 i = f c + 'h'f 

where Fc is the core admittance, given by equa¬ 
tion (52); Ym is the mechanical admittance (51); 
and $ is the turns ratio of the electromechanical 
transformer. In Figure 31, the straight, vertical line 
through O' represents and the motional circles 
represent the motional admittance ‘h-Fji/. It should 


be noted that the motional admittance is not the 
reciprocal of the motional impedance 

Z" 

y _ ein 

"mot ~ 'Z I ^ 

T 

and is not simply related to it. The spacing of 
points in frequency on the motional impedance and 
admittance circles is not the same. In the former, 
the spacing is determined by the Q of the total 
mechanical circuit with electromechanical coupling. 
In the latter, the spacing is fixed by the Q of the 
mechanical circuit without electromechanical cou¬ 
pling. Distinction will sometimes be made between 
these two quantities by writing them Qz and Qy 
respectively. In Figure 28, Qy applies to the series 
combination of the elements marked “mechanical” 
and “load”, while Qz includes, in addition, that 
marked “core.” In general, Qy is larger than Qz- 


3.6.1 DEDUCTIONS FROM ADMITTANCE 
DIAGRAM 


The admittance diagram can be used in the same 
way as the impedance diagram to obtain certain 
properties of the transducer. If it is assumed only 
that the mechanical .system shows a simple reso¬ 
nance of high Q, then, as already found in Figure 16 
of Chapter 2, the motional impedance loop is close 
to a circle. Since the admittance diagram is the 
geometrical inversion of the impedance diagram, the 
motional admittance loop is also a circle. It is 
found, from the geometrical properties of an in- 
vension, that 


'■^max 

C 

'^min 


^rnax 

^iniii 


(53) 


where and are the maximum and minimum 
conductance around the admittance circle, just as 
Rmax and 7?niiii are the maximum and minimum re¬ 
sistance around the impedance circle of Figure 16 
of Chapter 2. Equation (53) allows the potential 
efficiency of equation (62) of Chapter 2 to be written 
as 

n/(7 — Vg • 

Pot eff = (54) 

"^Gmax + "^Gmin 


The impedance diagram was used in equation 
(57) of Chapter 2 to find the actual efficiency of a 
transducer at resonance. A corresponding treatment 
of the admittance diagram gives the efficiency at a 
frequency close to /e, the frequency of maximum 


CONFIDENTIAL 










IMAGNETOSTRICTIVE VIBRATORS AND EOUIVALENT CIRCI ITS 


51 


efficiency. In the special case of the circuit of Figure 
28 and the simplified admittance diagram, Figure 31, 
the efficiency given is equal to the maximum effi¬ 
ciency. The general formula for the motional ad¬ 
mittance is Fmot = Here = 1/Zi is 

the loaded admittance of the transducer and 1% = 
1/Zc is the blocked admittance. With the helj) of 
equation (20) of Chapter 2 it is found that 


= Fi - F« - 


— 

Z/p 

7“ 

/jp 


(55) 


7„. + 7;. + 


Similarly, from ecpiation (21) or (55) of Chapter 2, 


Eff = 


7, - 7, 
/C 

Yi - F 

(' i 


lii 


7,„ -|- 7l I 

Rl 


Z,n -\- Z L -\- 


(501 


E(juations (55) and (50) are identical in form with 
e(iuations (40) and (55) of Chapter 2. The blocked 
electric impedance Zg and the mutual impedance 
Zgm are assumed to be slowly varying compared with 
Zm + 7l, which goes through a simple resonance at 
frequency Jr. The denominator of eciuation (55) is 
real (resonant) at a slightly different frequency Je- 
Here at Je, F^ot has its maximum magnitude equal 
to Dy, the diameter of the admittance circle. By 
the same process that leads from equations (40) anti 
(55) to (57) of Chajiter 2, it is found that efficiency 
at Je is 


Eff;, = 


/Diameter admittance circle in water 


X 1 - 


\ C’onductance at Je in water 

Diameter admittance circle in water 
Diameter admittance circle in air 


(57) 


Note the similarity between equation (57) and 
etiuation (57) of Chapter 2. In general the admit¬ 
tance formula gives a somewhat higher efficiency 
than the impedance formula, since Je is usually 
closer to Je (maximum efficiency) tlian is Jr (reso¬ 
nance). From equation (22) of Chapter 2 it is found 
that 


Am + A'i — 


sin 2C,„ 
2 sin fe 


(at Je) ; (58) 


where the phases and .Com are defined through 

7, = I 7, I , 7.m = I 7,m I . (59) 


The reason for choosing the phases in this particular 
way is that they both become ecpial to the eddy- 
current angle C when the transducer under con¬ 
sideration is a ring with negligible leakage inductance 
and copper losses. At fre(iuency Je 


A'm 4- A L 


I cos (Co - 2Com) (at J'e) . 

1 


(GO) 


At resonance, of course. 


Am + A'l — 0 (at Jr). 


The ratio of equation (GO) to (58) is 


(Am “b ^ E I ^ Sin 2(^0 Com) 

(YJit 4“ A/.)A’ sm 2(, ,.m 


Thus E' may lie abo\-e or below E. When Co = Com, 
E' and E are coincident and equation (57) gives the 
maximum efficienev. This will happen, in general, 
only when leakage inductance and copper resistance 
can be ignored and when there are no important 
shunt elements exce])t the core impedance, fn most 
of the applications here, ideal conditions will be 
assumed and equation (57) will be interpreted 
as the maximum efficiency. An ea.sy test which 
tells whether Je and Je are close together is to note 
the inclination of the principal diameter of the 
admittance circle. According to equation (55), 


Inclination of principal admittance diameter 

= 2(Ce-C™)- (Gl) 


Thus, when the principal diameter is horizontal, 
fe and fpm are equal and eriuation (57) gives the 
maximum efficiency. 


.3.7 COMPARISON OF IMPEDANCE AND 
ADMITTANCE METHODS 

In this section the principal differences between 
the impedance and admittance methods are outlined. 
In what follows it has lieen assumed that the 
mechanical system goes through a simple resonance 
and that the tdocked electric impedance and the 
mutual impedance are constant in comparison. A 
further specialization is made in that and of 
equation (59) are taken as equal. This is tanta¬ 
mount to omitting leakage inductance and copper 
resistance and using the circuit of Figure 28 in which 
the mechanical arm has high Q. 


CONFIDENTIAL 


















COMPARISON OF IMPEDANCE AND ADMITTANCE METHODS 


3.7.1 Principal Points of Difference 

between Iinpedanee and 
Adinittanee IMethods 

1. The core admittance in the region of small 
eddy currents is a straight line; the core impedance 
is the arc of a circle. 

2. The principal diameter of the motional ad¬ 
mittance circle is horizontal; the principal diameter 
of the motional impedance circle is inclined. 

3. The principal diameter of the motional admit¬ 
tance circle ends in the point of maximum efficiency, 
which is the efficiency most readily obtained by the 
admittance method. The principal diameter of the 
motional impedance circle ends in the point of re.so- 
nance and it is the efficiency at resonance which 
is most easily found by the impedance method. 

4. The mechanical Q found from the admittance 
diagram does not include damping from eddy cur¬ 
rents; the Q from the impedance diagram does 
include this damping. 

5. For small eddy currents, core conductance is 
constant and the diameter of the motional admit¬ 
tance circle is a good index of potential efficiency. 
Since core resistance does change with frequency, 
the diameter of the motional impedance circle is not 
an index of potential efficiency. 

0. If copper resistance and leakage reactance are 
not negligible, it is more difficult to take them into 
account in the admittance method than in the 
impedance method. 

7. If copper resistance is neglected, zero fre¬ 
quency falls at infinity in the admittance diagram 
and at origin in the impedance diagram. 

3.7.2 SuDiniary of Formulas for 

Impedance Diagrams 

1. Potential efficiency 

_ 

V/f -b V/? ■ ' 

where ^^min fii’f die maximum and minimum 

resistances on the impedance circle. 

2. The Q of the mechanical system including 
damping due to eddy currents (Qz) is 

Frequency of resonance 
Difference between frequencies at 
ends of diameter perpendicular to 
resonance diameter 


3. Efficiency at resonance 


Da — D\r ^ 
R. Da 


(64) 


where /f, = resistance at resonance in water, 

D\y = diameter of impedance circle in water. 
Da — diameter of impedance circle in air. 


3.7.3 Summary of Formulas for 
Admittance Diagrams 


1. Potential efficiency 


Vg - Vg ■ 

^ '^max ^ '-'min 

Vg 4- Vg • 

^ max I ^ nim 


(65) 


where G^ax; f?min iii'P the maximum and minimum 
conductances on the admittance circle. G,nin is also 
the core conductance G^, and is G^ -f Dy, the 
sum of the core conductance and the diameter of the 
admittance circle. 

2. The Q of the mechanical .system excluding 
damping due to eddy currents (Qr) is 


Frequency of maximum efficiency 
Difference between frequencies at 
emls of diameter perpendicular to 
efficiency diameter 


3. Maximum efficiency 




(67) 


where Da and Dr are the diameters of the admittance 
circles in air and water, and Gj = Gc D\y = G^ax 
is the maximum conductance in water. 


3.7. t Kelation between Impedance 
and Admittance Diagrams 

In the following. Re, Xc are respectively the core 
resistance and reactance, with leakage impedance 
assumed to be negligible; Gc and Be are respectively 
the core conductance and .susceptance; Dz and Dy 
are the diameters of the motional circles in the 
impedance and admittance diagrams respectively; 
and Qz, Qy, are the Q’s for the motional circles in the 
impedance and admittance diagrams respectively. 
It is assumed that the principal diameter of the 
admittance circle is horizontal, i.e., that eciuation 
(61) is zero. 


CONFIDENTIAL 











36 


MAGNETOSTRICTIVE VIBRATORS AM) EQUIVALENT CIRCUITS 


1. Diameters of circles: The diameter of the 
admittance circle is related to quantities in the 
impedance diagram l\y 


Dy = 


D. 


~ licDi 


( 68 ) 


The diameter of the impedance circle is related to 
quantities in the admittance diagram by 


Dz 


Dy 

Di -V Be + G, Dy 


(69) 


2. Mechanical Q’s: The Q measured from the 
admittance circle Qy, which excludes damping due to 
eddy currents, is related to im])edance data by 


Qz{I{l + Xl) I / DzXe 
R't + X'i - RrDz ' ^ (hiR'i + A'-) ■ 


(70) 


The Q measured from the impedance circle, which 
includes damping due to eddy currents, is related to 
admittance data by 


Qz 


QyjGl + Bl ) I / _ DyBe 
ai + Bl + DyGe\ Qy{ai'+Bl)' 


3. Frequencies of resonance and maximum effi¬ 


ciency : 


yV ^ I ^ DzXc 

^-1 {Rl + Xl)Qz 


^ 1 - 


DyBc 


{G~ + Be)Qy 

^ n/ 1 — A'/ff 


(72) 


where//f is the frequency of resonance, Je is the fre- 
cpiency of maximum efficiency, and A^ff is the effec¬ 
tive coefficient of electromechanical coupling. 

4. Effective electromechanical coupling: 


A 


eff 


! Dz ^ | / Dy 
X,Qz i BeQy' 


(73) 


Effective coupling will be discu.ssed in the next sec¬ 
tion. 

o. Relation between efficiency at re.^onance and 
maximum efficiency: 


Pff _ 7fr(Rc ~l~ A~) + {Xl — R~)Dz 
" “ IGiRl + Xc) + R'iDz 


Ri + xi 


Rl + Xl - ReDz 


■ Effrps 


/fc +A? 


Rl T Ac — RrDz 


Eff. 


Eft’res 


( {Ge + DY){Gl + Bl) \ 

\Gr{Gl + Bl) + BiDy) ■ 

( gi + b: \ 

XGl + Bi + GrBy) ^ 


+ Be 


G] + Bi + GrDy 


-) Eff„ 


(75) 


where all quantities refer to the admittance diagram 
in water. 


3.8 TRANSDUCER AS BAND-PASS 
FILTER: EFFECTIVE COUPLING 

The circuit used previously in the discu.ssion of 
impedance and admittance diagrams is reproduced 
in Figure 32. Its elements are simplj' related to 



Figure 32. Elements of equivalent circuit from ad¬ 
mittance data. 


quantities easily found from the admittance diagram 
and have been labeled. If only impedance data are 
available. Figure 32 may still be used with the help 
of conversion formidas given in the previous section. 
In Figure 33, a shunt conden.‘;er with capacity 
Bc' ue, together with a generator, has been connected 
to the electric terminals. The portion of the circuit 



I 


CTnnn I I 1 

l/Gg 

IBcA^EI 

1 

1 


^ VVV j 1 J 

1 

■|/Bc“e i 

i 

i 


1 

! 


1 


Figure 33. Transducer as hand-pa.ss filter. 


between the dotted lines is seen to be a band-pass 
L .section, which, since the resonance of the series 
arm and the antire.sonance of the shunt arm coincide, 
is of the constant-/^ type. The width of its pass 
band is given by 


ih - /.) ^ \ ^ 

h ' QyBc 


(76) 


where all cpiantities refer to the impedance diagram where fo and /i are the nominal cutoff frequencies 
in watei-. and where Ay^ will be called the effective coefficient 


COXFIDEXTIAL 










































TRANSDUC.KK AS HAND-PASS FILTER: EFFECTIVE COUPLINi; 


of electromechanical coupling for the transducer. 
The im age impedance at midhantl frequenc}^ 
/«(= fifi) is _ 

^ DyB, 

Now the best baml-pass behavior of the filter will bo 
obtained if it is terminated on both ends with a 
resistance close to K. (A slight mismatch ma}^ 
be deliberately introduced in the right direction in 
order to hold up the response near cutoff.) The 
termination on one end consists of the resistance 
\/Dyw (the reciprocal of the admittance diameter 
in water). Therefore, it is desirable that 


Dyw — Bckgff. 

On the electric end, the filter is terminated by the 
resistance l/Gc in parallel with the generator. If 
the generator resistance is 1-Gg, proper termination 
indicates 

G„ — 5A-eff - Gc 


The efficiency when the transducer is terminated 
for optimum characteristics as a filter is less than 
the potential efficiency which would be obtained if 
the termination were optimum for efficiency. The 
two efficiencies can be found from equations (65) 
and (67). They refer to the tran.sducer itself and 
do not include any losses incurred in the generator. 
Thus 


Band-pass eff 
Potential eff 


1 


1 + 


Go 

Bckf.fi 


Bckeff 

Da 


1 + 


2Gc 

7^ 



D^f 


(77) 


When the transducer has small mechanical losses. 
Da is large and the second factor is close to unity. 
If eddy-current losses are also small, Bc/Gc is large 
and the first factor is near unity. If both conditions 
apply, the loss in efficiency is small. 

The effective coefficient of electromechanical cou¬ 
pling defined by 


kf.ff 


Df 


BcQf 


Di 


XcQi 


(78) 


is a useful and important quantity which can be ob¬ 
tained directly from impedance or admittance data. 
Note that D/Q remains constant as the load resist¬ 
ance is varied, so that equation (78) can be applied 


to measurements either in air or water, provided, as 
has been assumed, the water adds a purely me¬ 
chanical resistance. The effective coupling is closely 
related to k, the coupling coefficient for the mag- 
netostrictive material. From equation (15) 



where X is the magnetosfrictive constant, n the 
permeability, and E Young’s modulus. For the 
cylindrical transducer, 

kf.n = 4^-- 

The factor xo/V^x/f within 1 per cent of unity if 
the frequency/is less than/c, the characteristic fre¬ 
quency for eddy currents, and if the departure does 
not roach 10 per cent until ///<• is greater than 3. 
Thus, in any reasonably well-designed cylindrical 
transducer, kf,ff is nearly as large as k. 

For other forms than the toroid, the relation 
becomes more complicated, since such effects as de¬ 
magnetization and leakage, as well as the geometrical 
form, introduce numerical factors which reduce Av^ 
with resi^ect to k. With good design, this reduction 
is not large and the nearness of k^a to k is one of the 
criteria of excellence for a transducer. 


3.8.1 Representation of Foree by 
Current and Veloeity by Voltage 

It will be recalled that there is a fundamental 
difficulty in obtaining an equivalent electric circuit 
for an electromagnetic or magnetostrictive trans¬ 
ducer when forces are replaced by voltages and 
velocities by currents. This arises from the opposite 
signs of the mutual impedances with these types 
of electromechanical coupling. The difficulty was 
avoided in the magnetostrictive ca.se by the de¬ 
vice of rotating the phase of the force and velocity 
through 90 degrees before converting them to voltage 
and current. 

Earlier in this chapter it was noted that an alter¬ 
native method is to represent force by current and 
velocity by voltage. The chief objection to doing 
this is that complex mutual impedances are very 
difficidt to include, since an ideal transformer whose 
impedance ratio is complex is required. However, 
when the phase of the mutual impedance is small 
it can, without much error, be .set equal to zero. 


CONFIDENTIAL 


















58 


MAGNETOSTRICTIVE VIRRATORS AND EQIIVAEENT CIRCUITS 


With this simplification, the impedance of the 
transducer can be represented by the circuit of 
Figure 34. The series arm represents the blocked 
impedance, including both leakage and core imped¬ 
ances. This is in contrast to Figure 32, where 




^ -- wy w -- 

Dz/Oz“r ^ 



■i- i 




FiGrRE 34. Elements of equivalent circuit from imped¬ 
ance data. 


leakage had to be omitted. On the other hand, 
while Figure 32 gives a motional impedance circle 
with inclined resonance diameter, the resonance 
diameter for Figure 34 is horizontal. Thus, Figure 
34 will be the better representation if leakage is large 
but the eddj'-current angle and, hence, dip-of- 
resonance diameter are small. When these condi¬ 
tions are reversed. Figure 32 is superior. 

The band-pass properties of a transducer can be 
.shown with Figure 34 by much the .same method 
that was used with Figure 32. Since the blocked 
and motional impedances are in series and thus 
additive in Figure 34, it is convenient here to use 
impedance data, and the elements of the circuit have 



been so labeled. In Figure 35 a series-tuning, con¬ 
denser, with capacity 1 has been added, and 

the transducer has been attached to an electric gen¬ 
erator of resistance Rg. The portion of the circuit 
between the dotted lines is a constant-iv, band-pa.ss 
filter section. Its band width is 


h - /i 

fs 



(79) 


where /i, fi are the frequencies of cutoff and the 
center of the pass band is at re.^onance Jr = V/1/2. 


Thus equations (76) and (79) are in agreement in 
predicting a band width equal to the coefficient of 
coupling. The image impedance at midband is 


A' = 



Xf A'pff, 


and the filter is properly terminated when 
Dzw = ^ekeS 


and 


Ra 


^ek’en — Re- 


The efficiency is less than the potential efficiency by 
the factor 


Band-pa.ss eff 
Potential eff 


1 


1 + 


Re 

XX'eff 


D., 


2R, 

‘ + 57-- 


Da D\ 


which is similar in form and interpretation to equa¬ 
tion (77). 


3.8.2 Relation Between Maximum 
Effieieney and Effective Coefficient 
of Electromechanical Coupling 


Maximum efficiency with re.-^pect to frequency is 
given by 


Eff 


max 


Dyw a _ 

C, V Dya/ 


(80) 


where Dyw and Dya are the diameters of the ad¬ 
mittance circles in water and air respectively, and 
Gi is the total conductance in water at the frequency 
of maximum efficiency Je- Equation (80) is ob¬ 
tained from equation (57) under the a.ssumption 
that E and E' are coincident, that is, the principal 
diameter of the admittance circle is horizontal. 
Then, also, 

Gi = Gc DyWt 

where Gc is the core conductance. Thus, equation 
(80) can be written 



With the help of equation (75) 

_Gc _ 1 

^jur k-^fiQYwQe 


COXFIDEXTIAL 




























IMPEDANCE-ADMITTANCE DATA AND RESPONSE DATA 


59 


can be written where the abbreviation Qc = Bc/Gc 
has been used. Also, with the assumption that the 
water load is a purely mechanical resistance, 

Byw _ Qrw 

D YA Q IM 

Finally 



This formula is e.ssentially the same as equation 
(38) previously obtained for the ring. The first 
factor can be regarded as a gross electromechanical 
efficiency and the second as a mechanical efficiency. 
Note that the first factor increases with increasing 
Qyw> while the second decreases. The formula 
gives an insight into the conflict between the require¬ 
ments of high efficiency and low Q}-ir in magneto- 
strictive transducers where the effective coupling is 
low {k^n = 0.05 max). 

3.9 IMPEDANCE-ADMITTANCE DATA 
AND RESPONSE DATA 


ducer in order that they may be compared with the 
motional impedance and motional admittance (see 
Figure 36). The transducer has electric impedance 
Ze when open-circuited {v = 0) on the mechanical 
end; mechanical impedance Zm when open-circuited 
on the electric end; and mutual impedance Z,™. 
The relations involving these impedances have al¬ 
ready been discu.ssed in Chapter 2. The impedance 


-o o- 

-o o- 


Figure 36. Transducer as hydrophone. 



Zl in Figure 36 represents the radiation impedance 
presented to the face of the transducer by the water. 
The generator Fo represents the equivalent mechano- 
motive force acting in the circuit when the transducer 
is placed in a sound field. With the circuit equations 
(17) of Chapter 2, the open-circuit voltage at the 
terminals of the tran.sducer is found to be 


Z,„.F 

Zm + Zl.’ 


(83) 


In Chapter 1 it was .shown that the respomses of a 
transducer in transmitting and receiving are simply 
related when the transducer sati.sfies the reciprocity 
theorem and is linear in the range of operation in¬ 
volved. The connections which were found earlier 
can be written 

5/ = JlTy, 
aS^ = J iTj, 


200 

= — 10- 
pf 


1.94 X 10- 

fkc 


(82) 


where Sy = open-circuit (voltage) sensitivity (volts/ 
dyne/cm^), 

Si = short-circuit (current) sensitivity (am¬ 
peres/ dyne/cm^), 

Ty = voltage transmitting response (dynes/ 
cm^ at one meter/volt), 

Ti = current transmitting response (dynes/ 
cm^ at one meter/ampere), 

Jj = reciprocity parameter appropriate to 
distance of test of one meter, as used 
in transmitting response. 


The sensitivities Sv and Sj will be expressed in 
terms of the self and mutual impedances of the trans- 


and the current generated l)y the transducer when it 
is short-circuited is 


h = 



Zm + Zl + 


(84) 


Equations (83) and (84) could be used at once 
to determine *8^ and Sj if the connection between 
Fo and the pressure in the sound field (before the 
transducer is placed there) were known. In order 
to find this relation, the reciprocity theorem will be 
applied to the water between the tran.sducer and a 
simple source placed in front of the tran.sducer and 
at a sufficient distance to produce approximately 
plane waves. The arrangement is shown in Figure 
37. The two pairs of terminals at which connection 
is made to the water consist, first, of the face of the 
tran.sducer (denoted by the .subscript 1), and .second, 
of the surface of the simple source (designated 2), 
which may be taken as a .small sphere of area 
Suppose that 1 transmits through the water to 2 
and that 2 is stiff, so that its surface velocity is 
zero {v'i = 0). The mutual impedance is 


v[ v[ 


(85) 


CONFIDENTIAL 





















60 


MAGNETOSTKICTIVE VIBRATORS AND EQUIVAEENT CIRCUITS 


where is the force ajjplied to the medium at 2 
when its velocity at 1 is v[. The pressure in the 
water at 2 is p 2 - This is the same whether or not 2 
is present, since it is assumed small and stiff. Now 
let the transmission take i)lace in the reverse direc¬ 
tion, from 2 to 1. This time the velocity at 1 is 


O 

Vg = 0 


v;--o 
Fl' = F^ 


-A-► 

Figure .37. Reciprocity applied to transmitting 
medium. 


taken to be zero {v'i = 0). Then the force 
which 1 exerts on the water is the same as Fq, the 
mechanomotive force at 1 due to source 2 in the 
water. The mutual impedance here is 


V 2 v'-i 


( 86 ) 


According to the reciprocity theorem, the cpianti- 
ties in equations (8.5) and (86) are equal. Thus, 


F,= - 


c2P2 ^2 


(87) 


Now let the transducer 1 be removed and let the 
source 2 continue to transmit with surface velocity 
V 2 . Pressure p at the position which the transducer 
previousl.y occupied is, apart from pha.se. 


pcv'i 0-2 
2rX 


( 88 ) 


where pc. is the characteristic acoustic resistance of 
the medium, r is the distance between the two 
positions 1 and 2, and X is the wave length in the 
medium. Combining equations (87) and (88), 


Fo = 


2r^ 

pc 


(89) 


When tranisducer 1 is radiating, the power tran.s- 
mitted is 


v[ YRl 


Atti'-D \ P 2 
pc 


(90) 


where Rl is the radiation resistance for the trans¬ 
ducer and D is its directivity ratio. Equations (89) 
and (90) give the relation 


with 


= 2tr' 

\ V , 

(91) 

/ F' 

Rl 

(92) 



AwlJ 

pc 


The area a' is an effective area of the tran.sducer. 
It can be shown that cr' is ecpial to the actual area 
for any transducer whose radiating face is plane and 
lies in an infinite plane, stiff baffle. If the baffle 
conditions are not met but the radiating face is still 
plane, it can be shown that a' approaches the actual 
area cr as the ratio of the dimen.sions to the w^ave 
length is increased. 

Combination of ecpiation (91) with equations (83) 
and (84) allows the receiving sensitivities to be 
written 


Sv = 


and 



= 2<t' 


Z„. -b 


X 10- 




+ Zl + ~ 


X 10, 


(93) 


(94) 


where the factors 10“* and 10 take into account that 
the impedances Z^m and Ze make use of electromag¬ 
netic units, while Sy and Sz are expressed in terms 
of practical units. Equations (93) and (94) can 
also be obtained from ecpiations (27) of Chapter 1, 
(17) and (21) of Chapter 2, with proper attention 
to units. 

The motional impedance and admittance of a 
magnetostrictive transducer are given by equations 
(46) of Chapter 2 and (76), namely. 


Z^ 

^ mot = -^ • (96) 

Z^ + Zz + 


CONFIDENTIAL 































impp:dance-admittance data and response data 


61 


With the assumption that a' and | Zem | vary 
slowly with respect to frequency in comparison to 
1 + Zl |, it is seen that equation (93) and the 

magnitude of equation (95) change with frequency 
in the same way. Thus, the Q determined from the 
open-circuit receiving response Sy or the current- 


transmitting response T/ is approximately that ob¬ 
tained from the impedance diagram Qz. Similarly, 
comparison of equations (94) and (96) shows that 
Qy is approximately the same as the Q obtained 
from the short-circuit receiving response or the 
voltage transmitting response. 


CONFIDENTIAL 



Cliapter 4 

MAGNETIC AND MAGNETOSTRICTIVE PROPERTIES OF MATERIALS 


1.1 INTRODUCTION: TYPES OF 
MEASUREMENT 

This chapter is an account of the magnetic and 
magnetostrictive properties of a number of ferro¬ 
magnetic materials, as obtained from experiments 
carried out at the Harvard Underwater Sound Lab¬ 
oratory [HUSL]. Since the laboratory did not have 
facilities for making special alloys, studies were made 
only on materials available commercially and on 
small samples supplied through the courtesy of the 
International Nickel Company. 

Information was obtained in considerable detail 
for materials that were widely used at HUSL. It 
.should be emphasized, however, that only a few 
samples were measured of each material subjected 
to a given type of heat treatment, making it some¬ 
what difficult to judge how consistently a certain set 
of de.sirable properties can be reproduced in a given 
batch of material. For this reason the results 
described in this chapter should be regarded as 
representative rather than definitive. 

Three types of measurements were emjDloyed to 
obtain information about the characteristics of the 
materials. The first consisted of magnetic measure¬ 
ments of the u.‘ual kind by the induction method. 
Normal magnetization curves (commutation curves), 
major and minor hysteresis loops, and the reversible 
permeability at various intensities of polarization 
are obtained from this type of measurement. Such 
data are needed for the design of tran.sducers that 
emplo}^ somewhat complicated magnetic circuits, 
for a preliminary' study of the losses in magnetostric¬ 
tive transducers, and for checking the theory of a 
magnetostrictive transducer of simple construction. 

The second type is a static study of magnetostric¬ 
tion and is employed only when the material cannot 
be obtained in the form of rolled sheets of suitable 
width. In measurements of this type observation 
is made of the change in polarization at a steady mag¬ 
netic field for a given change in applied stress with the 
62 


sample in static equilibrium before and after each 
measurement. 

In the third type, which may be referred to as 
dynamic measurements, a ring sample, together with 
the primary coil wound on it, forms a transducer, 
and evaluation is made of the various coefficients 
from impedance or admittance bridge measurements, 
using the theory of a ring transducer. 

The electric resistivities of the various materials 
were measured and in certain cases a simple determi¬ 
nation of the density was also made. 

A comprehensive survey of magnetostrictive ma¬ 
terials has been made at the Bell Telephone Labora¬ 
tories Inc.^^' Their results should be compared with 
tho.se described in the present chapter. 

4.2 FUNDAMENTAL MAGNETO- 
MECHANICAL RELATIONS 

The phenomenon of magnetostriction has been 
discus.sed in some detail in Chapter 1, while the re¬ 
lation among stress, strain, and an applied magnetic 
field has been used exten.sively in the di.scu.s.sions of 
Chapter .3. In this section rigorous derivations of 
the fundamental magnetomechanical relations will 
be made in order to clarify the definitions of the 
various quantities obtained in the different tj'pes of 
measurements and the relations among these quanti¬ 
ties. 

L'nder the action of a magnetic field //, the .shape 
of a magnetostrictive body and its intensity of 
magnetization / are functions of H. Therefore, 
when external forces are applied to the body, both its 
shape and intensity of magnetization are functions 
of H and of the applied forces. 

For present applications, discussions will be 
limited to the change of linear dimension in the 
direction of I when the body is isotropic and when 
both I and the stress P in the material are parallel 
to H. In general, a change in linear dimension in 


CONFIDENTIAL 


fundv,mp:ntal aiagnetoaiechanical relations 


6:$ 


the direction of I is accompanied by similar changes 
of the opposite sign in the perpendicular directions, 
hence the change in volume can be neglected. Thus 
only the length L, which is measured parallel to II 
and P of the body, will be considered and the ecjua- 
tions of the state of the body can be written in the 
form: 

s = s{H,P,T) B' = B'{H,P,T). (1) 

If equations (1) can be solved, we can also write 

H = H{B',s,T) P = P{B',s,T), (2) 

where T = the absolute temperatiire, B' = 47r7 = 
B — H, and s = 8L 'Lo is the strain in the material. 

The Lq can be taken as the length of the body 
when it is demagnetized and free from magnetic 
field and stress or as the length of the body under the 
equilibrium action of a steady field Ho and a steady 
stress Po. 

From equations (2) the total differentials may 
be written as 



Here {dP ds)s ',t is Young’s modulus at constant 
temperature and constant polarization and will be 
denoted by E; (dP dP')^ ^ wid de defined as the 
magnetostrictive constant and denoted by —X. 

When B' is increased to B' + dB' and s to s + ds 
by small changes in H and P, the work (r/TT) done 
on unit volume of the material is given by 

dB' 

dW = H - + Pds. 

■i-rr 

From the fundamental law of thermodynamics, we 
have 

dP' 

dU = TdS + H -f- Pds, 

dir 

where U is the internal energy and S the entrop.y per 
unit volume. Hence the differential of the free 
energy F is given by 

dB' 

dP = -SdT + H — + Pds. 

dTT 

As dP is a total differential, it follows that for an 
isothermal change. 



Equations (1) state; If an increase in magnetiz¬ 
ing field should accompany a stretching (positive s) 
of the material in order to keep the polarization 
constant, a tension (positive P) must accompany 
an increase in polarization in order to keep the 
length constant. Hence X has the same sign as 
magnetostriction in the u-sual sense, namely, the 
change of length with polarization. The sign of X 
is immaterial for most application^, but a distinc¬ 
tion must be made whenever two different materials 
are used in the construction of one transducer. 

Using equations (3) together with the differentials 
of equations (2) and setting dT = 0, we can .solve 
for dB' and ds in terms of dP and dll. Thus 



or, 

_ /^\ 2, (^\ _ i 

\dH/p,T \ds / B'.T A \dP/n.T Vds/a'.rA 


(5) 



From the second and third parts of equation (5) 
and from equation (4), it follows that 

/dP'\ /ds\ 


which can be independently obtained from a con¬ 
sideration of the Gibbs’ thermodynamic potential G 
which satisfies; 

B' 

dG = -SdT - dll - sdP. 

■iir 

In the equations of state (1) and (2), H and P 
enter symmetrically. However, it is an experi¬ 
mental fact that an unmagnetized or demagnetized 
body cannot be magnetized simply by stretching or 
compression. In other words, stress has the sig- 


CONFIDENTIAL 









ma(;netic AM) ma(;net()stri(:tive properties ok materials 


61 


nificance of (iirectioii but not of senso. Thei’efore, 
at the point B = H = 0, {dB' dP)n,T = 0. It fol¬ 
lows from (6a) that {ds/dH)pT = 0, and from the 
third part of equation (5) that X = 0. Thus, for 
an unmagnetized body, small variations in B' do not 
set up any macroscopic stress in the body. 

Since, in the present applications, the active ma¬ 
terial of the transducer is subjected to no steady 
stress, P = 0, and it may be said that (dP' dH) p t 
= in' — 1), where )x' is the reversible permeability at 
constant stress, as is usually observed. In order to 
take account of hysteresis, /u' is here defined as the 
reversible rather than the differential ijermeability. 
The permeability at constant strain shall be denoted 
as M ~ 1 = With these abbreviations, 

it is found from the first, second, and last of equa¬ 
tions (5) and (6) that 


/dP'\ 1 

^ ^ ~ Vd//A.r ~ /dl 


dH \ 

,, .. 47rX‘-(M - 1)( 

-(m-D- - - -, > 


\ds/ii,T (ds 


(-) 

VdP///j 


= E 


1 - 


1 /dP'\ 

and A = (-) = 

\dF / a.T 


47rX“(^i — 1) 

E . 

47rX(^i' — 1) 


E 


(7a) 


(7b)“ 

(7c) 


In the a})ove equations, may be called the 
clamped core reversible permeability and E' Young’s 
modulus at constant magnetic field. Experimentally 
it is always and E' that are directly observed, since 
it is not practical to clamp the sample or to keep the 
magnetization constant. Moreover, it is A that is 
observed in static measurements, while X is of special 
interest in transducer theory. 

It will be seen that in the above discu.ssions all the 
differential coefficients considered should be called 
isothermal coefficients. In acoustic experiments, 
however, we deal with adiabatic conditions rather 
than isothermal. By a consideration of the internal 
energy and the enthalpy (total heat), it can be 


“ ThLs equation ts in agreement with equation (11) of 
Chapter 1, if it ts recalled that p is usually large compared to 
unity, so that ^ — 1 is approximately equal to p. 


.shown that relations similar to those of equations 
(4) and (6a) also exist in the adiabatic ca.se. 
Therefore, all the equations derit'ed above are ti’ue 
for the adiabatic ca.se if the .sub.script T of the 
differential coefficients is replaced by S. 

Experimentally, static measurements are made 
under i.sothermal conditions, while dynamic measure¬ 
ments are made under adiabatic conditions. How¬ 
ever, the adiabatic changes of temperature in 
practical cases are usually very small. Thus the 
difference between the isothermal and the adiabatic 
Young’s moduli for metals is usually about half of 
one per cent, while the magnetocaloric effect of a 
ferromagnetic material at a temperature far below 
its C'urie i)oint is scarcely larger than 1 per 1000 C. 
Such small effects are well within experimental error 
and it may be said that the adiabatic coefficients are 
approximately equal to the respective isothermal 
coefficients. 

In deriving the equation of motion of a tran.s- 
ducer, it is necessary to find a relation between the 
change of stress dP, the change in field dH and the 
change in strain ds. This can be found from equa¬ 
tions (3) {dT = 0) and (7). Thus, 

-dP = \dB' - Eds 

= — \)dH “b 47rX"(/i’ — l)c/s — Eds (8) 

= X(m' - l)dH - E’ds. 

In the second form of —dP in the last expre-ssion, 
the change of polarization dB' is divided into two 
parts, one due to the change of field dH and one due 
to the change of strain ds. In the ca.se of a tran.s- 
ducer, dH is an alternating field. Since the first 
part is in phase with dH, it is the second that pro¬ 
vides a transfer of electric energy into mechanical 
energy, or vice versa. Therefore, the coefficient 
47rX^(/i' — \) 'E is of fundamental importance. In 
practice, fx' is much greater than unity, hence the 
latter may be neglected and we may write 
k = E. Equation (8) is then similar to 

equation (14) of Chapter 3. 

In the third form of —dP, the effect of magneto¬ 
striction is taken account of in the modified Young’s 
modulus E', which should be used in calculating the 
resonant frequency of a transducer. 

It is clear from the above discussions that the re¬ 
versible permeability that enters into the theory of 
magnetostrictive transducers is the clamped-core i-e- 
versible permeal)ility m'- This fact should be kept 
in mind when a comparison is made between the 
reversible permeability deduced from impedance 


CONFIDENTIAL 












SAMPLES MEASURED 


65 


measurements at supersonic freciuencies, by the help 
of transducer theory, and that directly measured l)y 
the d-c method, since the latter is rather than 
The difference between the two is usually small, l)ut 
it can amount to more than 10 per cent when k is 
large. 

The foregoing discussions are based u])on the 
assum])tion that the polarization of a material is 
entirely reversible. Actually this is not ti'ue, owing 
to magnetic hystere.sis. At high freciuencies, the 
eddy-current effect also changes the nature of the 
induction in the material. As C'hapter 3 states, 
these effects are usually taken account of by re¬ 
placing fjL by where xo and f are c'ddy- 

current ijarameters and 17 is the hysteretic loss angle. 
It is obvious that such a replacement in the first part 
of —(IP in ecpiation ( 8 ) introduces an electric loss 
in the clami)ed core, and in the .second jiart it intro¬ 
duces a mechanical loss to the motion. That part of 
the mechanical loss which is due to magnetic hystere¬ 
sis appears as elastic hysteresis. Thus, a magneto- 
strictive material woidd normally have an additional 
elastic hysteresis cau.sed by its magnetic hysteresis. 
Note also that the Young’s modidus E' observed 
will be affected by the hysteresis and eddy-current 
effects. 

Becau.se of its importance, the coefficient 
k = E is frequently used as a criterion in 

the selection of magnetostrictive materials. It will 
be seen later that E and \ are not affected to any 
significant degree by the structural changes of the 
material, while the value of ^ at a given value of 
magnetization depends greatly upon the previous 
history (heat treatment and mechanical working) of 
the material. In seeking large values of k, therefore, 
the choice of material is mainly based on the value 
of X rather than of 

Prior to the development of the theory of mag¬ 
netostrictive transducers, experimental study of mag¬ 
netostriction was generalh^ made with tliree different 
types of observations: ( 1 ) the variation in the length 
of a free specimen with its magnetization, ( 2 ) the 
effect of constant stress on the magnetization curve, 
and (3) the so-called \E effect. As can be seen from 
the above discussions, the I’elations between such 
phenomena and X are not very simple. Therefore, 
in using existing literature as a guide, the reservation 
should be made that a material which appears to have 
the largest magnetostriction as judged from the 
results of j^revious studies may not be the best 
material for magnetostrictive transducers. 


t.3 SAMPLES MEASURED 

t.3.1 Nickel and Nickel .Vlloys 

The first group of materials measured in the cour.se 
of experimentation consisted of jiure nickel and its 
alloys. The.se included A-nickel, Z-nickel, and D- 
nickel, manufactured by the Intei’national Nickel 
Company, and an alloy of nickel and iron containing 
45 per cent of nickel by weight, commonly called 
45-Permallov and produced by Western Electric 
C’ompany, Inc. 

Chemical analyses were made only of the A-nickel. 
However, D-nickel is known to contain 4.65 per cent 
manganese,with the remaining impurities pre¬ 
sumably the same as those of A-nickel. The compo¬ 
sition of Z-nickel is not available but it is known to 
contain more carbon and certain other elements than 
A-nickel, so that it is correspondingly more .sensitive 
to mechanical working and heat treatment. More¬ 
over, Z-nickel can be age-hardened. Table 1 shows 
four .sets of analyses made on different stocks of 
A-nickel, including two samples that had been sub¬ 
jected to the regular oxide-annealing treatment 
frequently used in this laboratory. It will be seen 
from the table that the oxide-annealed treatment re- 


T.\bi.e 1. Analysis of different stock.s of A-nickel. 


Elements 

0.005-in. sheets 
as received 

2i-in. tubing* 
as received 

0.005-in. sheets 
oxide annealed 

ll-in. tubing* 
oxide annealed 

Xi 

98.89% 

98.71% 

98.70% 

98.69% 

Cot 

0.6 

0.6 

0.6 

0.6 

Si 

0.04 

0.04 

0.04 

0.03 

Cii 

0.07 

0.09 

0.08 

0.11 

Mn 

0.34 

0.32 

0.31 

0.35 

Fe 

0.09 

0.07 

0.08 

0.09 

S 

0.004 

0.004 

0.005 

0.005 

c 

0.04 

0.1 

0.02 

0.01 


*0.03o-in. wall thickness, 
t Apj)roximate; spectroscopic analysis. 


moved some of the carbon from the nickel, which was 
to be expected. Further discussion of the composi¬ 
tion and finality of the.se A-nickel samples will be 
made in the next section. 

A nickel rod }g in. in diameter and 22 cm long, 
believed to be similar in quality to the A-nickel, was 
used in the static measurements. 

1.3.2 Iron-Cobalt Alloys 

The second group of materials u.sed in the experi¬ 
ments consisted of iron-cobalt alloys containing small 


CONFIDENTIAL 












66 


MAGNETIC AND MAGNETOSTKICTIVE PROPERTIES OF MATERIALS 


amounts of vanadium as a third alloying element. 
Chemical analyses of these samples were not made, 
but their nominal compositions are as follows: 

1. 2V-Permendur; 49% Fe, 49% Co, and 2% V 

by weight. 

2. 6.5V-vicalloy: 41% Fe, 52% Co, 6.5% 

and 0.5% Ain by weight. 

3. 8V-vicalloy: 40% Fe, 52% Co, and 8% V 

by weight. 

A sample of an iron-cobalt alloy in. in diameter 
and 22 cm long containing 70% cobalt was also 
procured for the tests. This sample consisted of 
electrolytic iron of high purity together with cobalt 
of commercial quality (99.8% Co, with Fe and Ni 
constituting a major portion of the impurity). 

t t HEAT TKEATMENT 

One of two types of heat treatment, depending on 
the design of the unit, should be used for the mag- 
netostrictive material of the transducer. Since the 
magnetostrictive coefficient is zero at zero polariza¬ 
tion and the stress set up in the material by a vari¬ 
ation of the magnetizing field does not vary with the 
sense of the field if the material is operated at zero 
polarization, the active material of a magnetostric¬ 
tive transducer must be operated at a certain steady 
polarization Bq, unless it is to be driven by large a-c 
magnetic fields at half of the resonant frequency. 
This steady polarization can be obtained by a d-c 
field, a permanent magnet, or by previously mag¬ 
netizing the active material to saturation and bring¬ 
ing the polarization back to the remanence 

W hen d-c polarizing fields or permanent magnets 
are used, the material obviously shoukl be as soft as 
possible magnetically so as to save d-c power. An¬ 
nealing at 900 C to 1000 C for one hour is generally 
sufficient for this purpose. The oxide-annealing 
treatment is particularly beneficial for nickel, since it 
forms a thin oxide film of very high electric resistivity 
on the surface of the material. 

Regular laboratory practice is to anneal in air at 
900 C’ for 20 minutes. But since annealing in air 
forms no insulating film, high-temperature annealing 
of other materials is generally done in hydrogen, an 
atmosphere which usually improves the magnetic 
properties of the materials. 

When the material is to be operated at remanence 
it is desirable that the remanence be at least as great 


as half of the saturation value and that the coercive 
force and the reversible permeability at remanence be 
as large as possible. It is well known that many 
materials exhibit small remanence either in the cold- 
worked or the well-annealed state, while annealing 
at a temperature close to the recrystallization point 
gives the maximum remanence and somewhat higher 
reversible permeabilities than can be obtained in the 
cold-worked state, without at the same time re¬ 
ducing the coercive force too much. This type of 
treatment is called half hard. 

A detailed study of the proper temperature for this 
half-hard treatment was carried out on 2V-Per- 
mendur because the stock made a^'ailable to HUSL 
was belie\’ed to be from the first large-scale produc¬ 
tion of this material in the form of rolled sheets. 
This treatment was generally carried out in hydro¬ 
gen, although for nickel a hydrogen atmosphere is 
not necessary. 

The vicalloys are ternary alloys which form 
homogeneous solid solutions at high temperatures. 
At temperatures below 700 C, marked precipitation 
liegins to take jdace. By controlling the degree of 
l)recipitation, the mechanical and magnetic hardne.ss 
of the material can be controlled. In extreme cases 
these alloys can be made hard enough magnetically 
to become permanent-magnet materials. The heat 
treatment tlien becomes a hardening rather than a 
softening operation. 

Annealing was carried out in a partly muffled 
furnace with automatic temperature control. The 
samples were enclosed in a stainless-steel box through 
which hydrogen could l)e passed when necessary. 
In general, the temperature was accurately measured 
by a chromel-alumel thermocouple and the tempera¬ 
ture fluctuation was about 5 C. With the exception 
of the nickel rod ami the hydrogen-annealed 5-mil. 
A-nickel .samples, however, the cooling was not 
always done in hydrogen. 

t..5 EXPERIMENTAL PROCEDURE 

4.5.1 Form of Sample 

The samples measured were in the form of strips 
or rods and stacks of punched rings consolidated by 
an in.sulating cement, usually A'inylseal or Cycle- 
Weld. Strips were employed only for auxiliary 
studies of magnetic properties along the direction of 
rolling and for resistivity measurements. The two 


CONFIDENTIAL 



EXPERIMENTAL PROCEDURE 


67 


rolls previously mentioned were used in the static 
measurements. These were made from ^Q-in. rods 
ot the metals by swaging. Ring stacks were u.sed in 
both magnetic and dynamic measurements. With 
the exception of the 8V-vicalloy and the D- and 
Z-nickel samples, each stack contained more than 25 
laminations. Two 6.5V-vicalloy samples were in the 
form of scrolls, which were made by rolling up a 
long ^-in. rolled strip and consolidating it with 
bakelite after heat treatment. The results obtained 
on these samples represent characteristics along tlie 
direction of rolling, while those obtained on ring 
stacks repre.sent average characteristics in the plane 
of rolling. 

4.5.2 Majrnetic IMcasurenients 

Method Used 

Magnetic measurements were made by the well- 
known induction method, using a ballistic gal¬ 
vanometer with 24-second periods and a .sensitivity 
of 0.003 microcoulomb jier mm at 1 meter. A .50-mh 
standard mutual inductance was used to calibrate 



the galvanometer. For this purpose the .secondary 
of the mutual inductance was permanently con¬ 
nected in the galvanometer circuit and the current 
used in the ]H'imary of the mutual inductance was 
measured with a 1-ohm standard resistance and a 
potentiometer. A simple circuit of the whole ar¬ 
rangement is shown in Figure 1. 

For magnetizing rod or strip samples, an air-core 
solenoid was used, measuring about 80 cm in length, 
with an air-core 3.7 cm in diameter, and capable of 
])roducing a maximum field for continuous operation 
of 1,320 oersteds at 10 amperes. Two similar search 
coils were connected in oi)po.sition and placed .side by 
side at the center of the magnet. Before the sample 
was introduced into one of these coils, their relative 


positions were adjusted until a reversal of field gave 
no deflection of the galvanometer coil. In this way 
the directly measured quantity was 47r/ = B', rather 
than B. 

The demagnetizing factors of cylindrical rods are 
known ■*’ and hence the static measurements could be 
corrected, but there seems to be no existing litera¬ 
ture on the demagnetizing factors of strips, .so that 
data obtained on them are to some extent erroneous. 
These errors are believed to be small, however, since 
the lengths of the strips tested were generally large 
compared with their thicknesses. 

Measurements on ring samples were made in the 
following way. The sample was first covered 
smoothly by a thin silk tape. Secondary coils made 
of a fine insulated wire (No. 35 to No. 39 B & S) were 
tightly wound on top of the tape. In most cases the 
.sample had a cross section of 0.15-0.55 sq cm, so 
that a secondary of less than 30 turns gave sufficient 
.sensitivity for measuring B while one of le.ss than 200 
turns was adequate for measuring the reversible per- 
meal)ility. The .secondaries were again protected by 
silk tape and a primary of two layers of No. 22 or 
No. 20 insulated wire was wound on top. The ring 
samples were particularh^ well adapted to this type 
of measurement, but coils had to be wound on each 
sample, and it was not possible to use large enough 
fields to .saturate the .sample completely so that in¬ 
formation ordinarily obtainable from the .saturation 
value was lacking. Corrections for leakage flux were 
usually estimated and applied. 

The magnetic properties of a sample are generally 
studied by measuring three curves: the normal B-II 
or commidation curve, a major hj^steresis loop, and 
the reversible permeability as a function of field along 
the normal curve. Before measurement, the sample 
was first magnetized to near saturation and then 
demagnetized by continuously decreasing an alter¬ 
nating field to zero. 

The normal curve was then traced by increasing 
II in steps and measuring the B by a single reversal 
of //. Each reading was repeated after a few re¬ 
versals of the field. The normal curve is therefore 
tlie locus of the tips of the hysteresis loops traced 
out by maximum fields of A'arying magnitude. 

A major hysteresis loop is one obtained by the 
reversal of a maximum field that is large compared 
with the coercivity. It can be most readily measured 
when it is possible to change the primary current in 
steps in a single series of operations. This method 
was used with the circuit of Figure 1. 


CONFIDENTIAL 















68 


.MA(;NETIC AM) MAGNETOSTRICTIVE PROPERTIES OF MATERIVLS 


IXTERPRETATIOX OF RESULTS 

The term reversible permeability needs further ex¬ 
planation. First consider the initial portion of the 
magnetization curve. Lord Rayleigh found that 
if a small induction Bi is obtained at a small field Hi 
by increasing or decreasing the field, then the change 
in B by varying the field by a small amount AH in 
the backward direction can be given by 

AB = h'iAH + §a(A//)-, 

where and a are constants anti the second term is 
positive or negative according as AH is positive or 
negative. It is obvious that the first term in the 
above expression repre.sents the reversible part of 
AB and that juJ is the initial reversible permeability, 
while the second term represents the irreversible {^art 
of AB. If Hi = Bi = 0 and AH is an alternating 
field of amplitude AHi, then the magnetization curve 
traced out is a small lance-shaped loop which is 
symmetrical with respect to the origin and in which 
the major axis has a slope ^l'l + 3-2aA//i. The rema- 
nence is simply joccAHi. The same situation is ])re- 
sumably true for any point in the B-H plane, 
provided that AH is very small. In this general 


ments the current through the transducer is also not 
infinitesimal. 

When the material is polarized by a steady fieltl 
Ho and an alternating field of amplitude AHi is 
superposed, then, as AHi becomes large, an unsym- 
metrical loop is traced out. Such a loop is defined 
here as a minor looj). 

4.5.3 Static Measurements 

For the static magnetostriction measurements, the 
air-core solenoid mentioned in the foregoing section 
was used. A pair of spools were installed side by 
side in the central portion of the solenoid. Each 
spool had two sets of coil windings, one over the 
other. The first pair of coils, with 5,(325 turns, were 
u-sed for mea.suring and .V; the .second pair, with 
319 turns, measured B. The arrangement was such 
that any emf generated by changes in an externally 
applied field were balanced out. An endpiece was 
soldered to each end of the cylindrical sample under 
test, so that when the .sample was properly inserted 
in one of the spools, one endpiece could be rigidly 
clamped with respect to the solenoid and the spool. 



Tigure 2. Mountini; of .sample for dynamic mea.surement. 


case, however, p' and a both decrease with increasing 
B. The n' is thus a limiting value, and any measured 
value with a finite AH gives the sloj^e n' -|- }4aAH 
of the corresponding lance-shaped looj). However, 
for practical purposes such measured values are 
accurate enough if AH is small. In the present 
measurements, 2AH seldom amounted to 10 i^er cent 
of the main field. Note that in the l:>ridge mea.sure- 


On the other endpiece was attached a flexible wire 
which passed over a pulley to .sup])ort an aluminum 
])an. Change of magnetization was observed by 
loading or unloading the pan. 

eights of 100, 200, and 500 grams were used in 
measuring A. In general, hysteresis effect was pres¬ 
ent and increa.sed with the increased size of the load. 
Each reading was accordingly taken by loading and 


CONFIDENTIAL 












































EVALUATION OF FUNDAMENTAL QUANTITIES 


69 


unloading the sample several times until a steady 
change of magnetization was obtained. 


4 . 5 . t Dynamic INIeasurements 

After magnetic measurements had been made on 
a ring stack, the primary and secondary coils were 
remo\'ed. The sample under test was then freely 
suspended by three ecpially sjiaced loops of silk 
thread in a toroidally wound frame made of wood 
(see Figure 2). A primary c'oil was then wound on 
the wooden frame and the .sample was leady for 
dynamic measurements by an impedance or ad¬ 
mittance bridge. It is .seen from the theory of toroidal 
transducers that any external mechanical resistance 
acting uniformly on the toroidal core does not affect 
the values of the fundamental quantities X, m, and E. 
The fact that this method of .suspension reduces ex¬ 
ternal mechanical resistances does, however, make 
po.ssible increa.sed precision of mea.surement. 

The dynamic measurements reported here were 
made in the Electrical Measurements Department. 
For a detailed account of the procedure and the 
apparatus, .see Chapter 11. 

4.5.5 Resistivity and Density 

Both strips and punched rings were used for 
measuring resistivity. When a strij) was u.sed, two 
leads were soldered or welded to each end. Through 
one pair of leads a measured current of 0.50 to 1.00 
ampere was sent through the strip and the potential 
across the other pair of leads was measured with a 
potentiometer. In the case of a punched ring, the 
leads were soldered or welded at two diametrically 
opposite points on the ring so that the two halves of 
the ring formed two equal re.sistances in parallel. 
Owing to the small thickness of the samples, the 
absolute values of the resistivities are accurate to 
about 2 to 3 per cent, but the relative accuracy is in 
general about 1 j)er cent. 

The densities of A- and D-nickel are known. For 
the rest of the materials, approximate estimations 
were made by weighing a number of punched pieces, 
the dimensions of which were accurately known. 


4.6 EVALUATION OF FUNDAMENTAL 
QUANTITIES 

Before presenting the results it will be helpful to 
summarize some of the formulas of Chapter 3 for the 


special case of a toroidal transducer of which the 
magnetostrictive core has a radius a, length I, and 
wall thickne.ss b, and the winding consists of N 
turns. From these formulas n, k, and X can be 
1 ‘eadily evaluated from impedance or admittance 
data. 


1 . 


For impedance data: 

a. Clamped-core impedance Zc 


ju^2N-^blfxX 

a 


b. Frequency of resonance Jr = —I 

27r' M 

where M = total mass of toroidal core, 

2ir6/ 

K = stiffness factor = - E 

a 


2'n-bl 


F(1 - xrI-^). 


c. Diameter of motional-impedance circle 


\Z'J„ 

R,n + R 


d. Qz 


Vmk' 
Rm R L 


e. The electromechanical cou])ling coefficient 

47rXV . . . 

k = —— IS given by 
h 

Dz _ k^ xf, 

QzEc 1 — Xnk’ xr 

With a knowledge of the density of the core ma¬ 
terial, Young’s modulus E' at constant field can be 
immediately calculated. If the effect of magnetic 
hysteresis is neglected, then xr and xo can be read 
from the curves in Figure 1 of Chapter 3, since the 
eddj^-current lo.ss angle f is determined from the dip 
angle (= 2f) of the resonance diameter of the 
motional-impedance circle. Thus k can also be cal¬ 
culated immediately. 

Calculation of X calls for a knowledge of ju, which 
may either be obtained from d-c mea.surements or 
calculated from the clamped-core imiiedance at 
resonance, provided the effect of magnetic hj^steresis 
is again neglected. A better method is to ajiply the 
theory described in the first .section of Chaiiter 3 to a 
whole series of values of the clamped-core impedance. 
This method can be applied to data obtained at a 
given frequency for various intensities of polariza¬ 
tion as well as for those obtained at a fixed polariza- 


CONFIDENTIAL 









70 


MAGNETIC AND MAGNETOSTRIf TIVE I'ROPEKTIES OF MATERIALS 



H IM OERSTEDS 

Figure 3. MaKiietizatioii and iiermeahility of hard-drawn A-iiickol tuhiiiK, 1.5-iii. diameter, 0.035-in. wall. Mag¬ 
netized circumferentially. 



-20 0 20 40 60 80 100 120 140 160 

H IN OERSTEDS 

Figure 4. Hard-drawn A-nickel tuhing, 23^-in. diameter, 0.035-in. wall, magnetized circumferentiallj'. 


tion for various freciuoncies. Also, it furnishes 
somewhat independent values of the resistivity and 
the reversible permeability. A quite different value 
of the resistivity is frecpiently obtained by this 
method as compared to that directly measured. 


2 


For admittance data: 
a. Frequency of maximum 


Ie = 




I 


efficiency 


where K = stiffness factor = 


2wbl 


E. 


a 


b. Diameter of motional admittance circle 




Dy 
C. Qy = 


e:;, + Re 

Vmk 


R + Re 

(1. The coefficient of electromechanical cou¬ 
pling A' is given by 


'Dy 




Qy (Arc + B^)xk 


CONFIDENTIAL 








































































































DISCUSSION OF RESULTS 


71 


Ill this case, xn can be determined by the type of 
geometrical construction shown in Figure 3 of 
C hap ter 3 or from the clamped-core admittance Yc 
at the frequency of maximum efficiency. The effect 
of magnetic hysteresis is again neglected. The values 
of M can also be found by a study of the clamped- 
core admittance. 

4.7 DISCUSSION OF RESULTS 

4.7.1 Method of Presentation 

The results obtained in the.se investigations are 


presented in Figures 3 through 48. These figures form 
two groups, one showing the general magnetic proiier- 
ties and the other the magnetostrictive properties of 
the various materials. There are more samples shown 
in the first category than in the second, but for every 
.sample that appears in the magnetostrictive group, 
there is a corres])onding set of curves for the mag¬ 
netic grouj). In order to facilitate comjiarison, curves 
for several samples are sometimes plotted in a single 
figure, but curves for one sample are .sometimes re- 
jieated in several figures. 




C()NFIDENTL\L 

















































































































MAGNETIC ANT) MAGNETOSTRKTIVE PROPERTIES OF MATERIALS 




H IN OERSTEDS 

Figure S. Reversible permenhility of A-iiickel sheets as affected by thickness and annealing conditions. 


CONFIDENTIAL 




























































































































































DISCUSSION OF RESULTS 


73 


Since the figures represent the properties of the 
various samples in sufficient detail, it will not be 
necessary to discuss all of them individually. Supple¬ 
mentary e.xplanations will be made of details that 
cannot be shown in the figures, and special attention 
will be given to the consistency with which results can 
be reproduced and to the agreement between experi¬ 
ment and theory. 


t.7.2 Magnetic JMeasurements 

Nickel 

.\s will be seen by the three A-nickel samples shown 
in Figures 3, 4, and 5, different stocks of the same 
material do not have identical magnetic jiroperties. 
Judging by the initial values of the reversible perme¬ 
ability, these samples are seen to have approximately 
the same magnetic hardness. The coercive forces are 
markedly different, however, causing variations in 
low-induction permeability. Differences in high-in¬ 
duction permeability also appear. These differences 



Figure 9. Ring laminations 0.005 in. thick of .\-nickel. 


since chemical analyses of the samples as shown in 
Table 1 are markedly uniform. In any case, it must 
be expected that similar differences will exist to some 
extent after heat treatment, particularly when sam¬ 
ples are not fully annealed. 

It is well known that nickel can be made magnet¬ 
ically very soft by high-temperature annealing in 
liA'drogen. Examjiles are the nickel rod of Figure (> 


and one of the o-mil A-nickel ring stacks of Figures 7 
and 8. 1 hese samples were annealed one hour at 
1000 (1 in hydrogen, cooled to 400 C at an approxi¬ 
mately uniform I’ate in 10 hours, and then removed 
from the furnace. The rod had an initial permeability 
of 370 and was practically saturated at a field of 20 
oersteds. Probably because of differences in size and 
orientation of grain, the sheet sample did not become 
as soft as the rod. 

There is a limit to the degree of annealing to be 
done in reducing internal strains in order to soften a 
magnetostrictive material, since in cooling the ma¬ 
terial through its Curie point internal strains are set 
up spontaneously b}^ virtue of magnetostriction. Ac¬ 
cording to Becker and Kersten’s theory,'*® the maxi¬ 
mum value of initial permeability M/max can be esti¬ 
mated from 


where 7, is the saturation magnetization, E Young’s 
modulus, and Sj the total fractional change of length 
at saturation of a free samjile as a result of magneto¬ 
striction. Taking 7^ = 510, E = 2 X lO'^, and the 
somewhat uncertain value of 30 X 10^® of s, for nickel 
yields Mimax = JOS. Thus the nickel rod apiiroaches 
the limit of magnetic softness. 

If the nickel rod is taken as standard for fully an¬ 
nealed nickel, the oxide-annealed samples shown in 
Figures 7 to 11 appear to be only partially annealed. 
This is probably due to the short time during which 
the latter samples were held at the high temperature. 

In Figures 7 to 11, No. 3 of the 5-mil samples was 
actually annealed 30 minutes in hydrogen and 10 
minutes in air at 900 C. All other samples went 
through the regular oxide-annealing process (20 min¬ 
utes at 900 C in air). The two 10-mil samples were 
actually from a single batch of punched rings an¬ 
nealed at the same time. It can be seen that the five 
oxide-annealed samples differ magnetically among 
themselves. However, one point seems to be quite 
definite: the 10-mil stock becomes magnetically softer 
than the 5-mil stock after the oxide-annealing treat¬ 
ment. 

The research laboratories of the International 
Nickel Company®® made chemical and physical tests 
for HUSL on four batches of oxide-annealed 10-mil 
A-nickel stampings which showed differences in mag¬ 
netic properties similar to those in Figures 7 to 11. 
Abnormality of chemical composition was absent, 


CONFIDENTIAL 





























































7i 


MAGNETIC AM) MAGNETOSTRICTIVE PROPERTIES OF MATERIALS 


tliickness of the oxide film varied from 0.00006 in. to 
0.00025 in., and the ^’ickers hardness number varied 
from 63.1 to 82.6. It would seem, then, that the dif¬ 
ferences in mechanical and magnetic hardness of the 



Figure 10. A-nickel tube, 1..5-iii. diameter, 6.0 in. 
long, 0.035-in. wall, magnetized longitudinally and cir- 
cumferentialh^ 


oxide-annealed samples are largely due to differences 
in the previous history of the stock materials. More¬ 
over, the short annealing period jtrobably makes the 
control of heat-treatment conditions difficult and this 
causes small differences. 



Differences apparent in the two 10-mil samples 
(Figure 7) indicate that small differences will almost 
always be present in different samples because of 
slight nonuniformity in the stock itself. These dif¬ 
ferences .seem to occur at low inductions so that they 


are relative!}^ unimportant and will affect the trans¬ 
ducer only when it is driven hard, since in actual 
practice the active material of a transducer is gen¬ 
erally polarized to a high intensitv (Bo — 4,000 for 
Ni).' 

Evidence of the effect of j)referred orientation is 
exhibited by the data obtained on the tubing shown 
in Figures 10 and 11. The two normal curves cross at 
B' = 5,300. When corrected for demagnetizing fields, 
the curve for longitudinal magnetization should ha^'e 
a larger ijortion hung above the curve for circumfer¬ 
ential magnetization than is shown by Figure 10. 














>\o 

















- 1 HR AT 1000 C IN 
—OXIDE ANNEALED 6 

Ht 

MIL 




\ 




^ 

, 10 

MIL 

^ 




-- 

























o 


























































•>«» 













% 





























'X 

- 1 




0 2500 g, 5000 

Figure 12. Permeability of O.OO.o-in. .\-uieke! ring 
lamination.s. 

Thus magnetization at high induction is easier along 
the axis, which means that the direction of ea.s 3 ' orien¬ 
tation of the crystallites tends to coincide with the 
axis of the tubing. A similar effect pre.sumably exists 
in the sheet samples, but, since measurements were 
made on ring samples containing a large number of 
laminations, the effect would be averaged out. 

It is generally accepted that the reversible perme¬ 
ability ix is a function only of the magnetization I, so 
that for a given \-alue of I, n should have the same 
^’alue whether measured at a point on the normal 
curve or on either branch of a major hysteresis loop. 
This should certainly be true for well-annealed ma¬ 
terials since hysteresis is small in such materials. For 


CONFIDENTIAL 























































































































































DISCUSSION OF RESULTS 


hard and half-hard materials, however, peculiar hys¬ 
teresis effects exist as exemplified by Figure 17. 
Smith has also found that if ^ is plotted against 
B - H the result approximates a straight line. Such 
an approximate relationship may .sometimes be useful 
for practical ])urposes. As Figure 12 indicates, this 
seems to be true for the cases of the hydrogen-an¬ 
nealed and oxide-annealed 5-mil A-nickel, but con- 


magnetization, even though the Curie point lowers at 
the same time.^® 

As can be seen by comparing Figures 14 and 15 
with Figure 5, the 20-mil D-nickel sample in the hard- 
rolled state is magnetically softer than the 5-mil A- 
nickel sheets. But this may not mean that D-nickel 
cannot be made harder. On the other hand, the 1000 C 
annealing made the material extremely soft with an 



H IN OERSTEDS 

Figure 13. Magnetization and permeability of Z-nickel. 


siderable deviation is present in oxide-annealed 10- 
mil A-nickel. 

From correspondence with E. AL Wise of the Inter¬ 
national Nickel Company, it was learned that the 
special features of Z-nickel are its higher mechanical 
hardness (20 to 35 Rockwell C) obtainable by me¬ 
chanical work and aging and its higher resistivity. 
The maximum coercive force obtainable in this ma¬ 
terial is about 48 as compared with 42 in A-nickel. 

The annealed sample of Z-nickel shown in Figure 
13 was treated at 1050 F and ciuenched from that 
temperature. The other sample in the figure was 
quenched from the same temperature and aged at 
485 F for 10 hours. As seen from the curves, the aged 
sample, presumed to be mechanically harder, shows a 
higher reversible permeability than the cpienched 
sample. 

The D-nickel is of particular interest because pre¬ 
vious investigations .showed that ^mall amounts of 
dissolved manganese in nickel increase its saturation 


initial permeability close to 700. As the saturation 
value was only about 10 per cent greater than that of 
A-nickel, Becker and Kersten’s theory already cited * 
predicts that the magnetostrictive effect has been re¬ 
duced. It will be seen later that this is true. 

The laboratory’s primary interest in half-hard ma¬ 
terials was their u.sefulness for transducers operated 
at remanence. For this purpo.se, the remanence 
shoidd be fairly high since the magnetostrictive co¬ 
efficient generally increases with increasing polariza¬ 
tion. At the same time, the coercive force and the re¬ 
versible permeability at remanence should also be 
large so that the remanence can be kept permanent 
and the electromechanical coupling coefficient can be 
large. These requirements are in some respects con¬ 
flicting, because the various quantities cannot be con¬ 
trolled independently. In general, an increa.se in coer¬ 
cive force or in remanence is accompanied by a drop 
in the reversible permeability at remanence. There¬ 
fore, the practice has been to anneal at such, a tem- 


CONFIDENTIAL 








































































76 


!MAf;NETIC AND AlA(;NETO.STKlCTIVK PKOl'EKTIES OE MATERIALS 



H IN OERSTEDS 

Figurf, 14. Hysteresis and permeability of D-nickel as received. 


Figure lo. 
He = 0.24. 


(I) 



porature that the remanent majiiietization i.s high 
without too great a sacrifice in coercive force. 

Figures 16 and 17 .show that tlie range of annealing 
temperatures for 5-mil A-nickel within which the 
remanence increases is rather narrow. A comparison 
with Figure 5 shows that only a slight change from 
the unannealed state re.sults from annealing for one 


hour at 550 C’. On the other hand, annealing at 620 C 
for one hour gives a lower value of the remanence 
than for the 600-degree anneal and reduces the coer¬ 
cive force to below 20. The critical temperature must 
therefore be very close to 600 C. One hour at this 
temperature incBfases the remanence by more than 
10 per cent and the reversible permeability by more 


CONFIDENTIAL 






















































































DISCUSSION OF RESULTS 


77 



-40 0 50 100 130 

H IN OERSTEDS 


Figure 16. Half-hard A-nickel sheets 0.005 in. thick. 



B-H 


Figure 17. Permeability of half-hard A-nickel sheets 
0.005 in. thick. 


than 30 per cent, and decreases the coercive force by 
about 20 per cent. It will be seen later that the one- 



H IN OERSTEDS 


PhGURE 18. Magnetization and permeability of hard- 
rolled 45-Permalloy sheets 0.005 in. thick. 


hour anneal at 600 C does improve the overall effec¬ 
tiveness of the material for operation at remanence. 
Data on 45-Permalloy are presented in Figures 18, 19, 
and 20. 


Iron-Cobalt Alloys 

Previous investigations on the fractional change of 
length as a function of magnetization show that iron- 
cobalt alloys with about 40 to 70 per cent cobalt con- 


CONFIDENTIAL 






































































































































78 MAGNETIC AM) MAGNETOSTRICTIVE PROPERTIES OF MATERIALS 


tent have the largest magnetostriction. According 
Masiyamad* the maximum occurs at a cobalt conte 



annealed in hydrogen 1 hour at 1000 C. 

to be magnetically hard and mechanically very diffi¬ 
cult to work. Furthermore, it is difficult to reproduce 



o in. in diameter. In spite of high-temperature anneal- 
it ing (identical with that for the nickel rod), the re- 
n versible permeabilities seemed to be rather low for a 
material with such a high saturation value. The pe¬ 
culiar manner in which the reversible permeability 
of this .sample varied with polarization was not ob- 
•served in any of the other materials. 

Previous investigators found that the addition of a 
small amount of vanadium im]n-oves the mechanical 
workability of the iron-cobalt alloys. With special 
heat treatment, the magnetic properties of some of 
these ternary alloys can also be improved.These are 
the reasons for the development of 2\’-Permendur, al¬ 
though this material was not originally developed for 
magnetostrictive transducers. 

For the ternary alloys with a constant cobalt con¬ 
tent of 50 per cent, Koester and Lang found that 
the a-y transformation temperature lowers with 
increasing vanadium content. When the vanadium 
content increases bej’ond 2 per cent, temperature 
hysteresis in the a-y transformation becomes quite 



H IN OERSTEDS 


.00.5-in. 4.5-Permalloj' sheets. 


empirical facts seem to be borne out in the 70% Co, 
30% Fe rod .seen in Figure 21. The original test sam¬ 
ple, 3-^ in. in diameter and 22 cm long, was made with 
considerable difficulty by swaging from a piece 


large. For this reason, the high-vanadium alloys can 
be hardened by partial precipitation, whereas well- 
annealed 2V-Permendur is soft because it contains 
a single a phase. 


CONFIDENTIAL 

























































































































DISCUSSION OF RESULTS 


79 


Of the 2V-Permendiir samples measured, those 
shown in Figures 22 through 27 were made from the 
first batch of 0.006-in. sheets obtained from BTL, 
while the remainder were made from a larger stock 
supplied by Western Electric Company, Inc. In this 
ca.se, the normal curves of the .soft-annealed samples 
again show considerable differences which are some¬ 
what exaggerated by the large differences in the coer¬ 
cive force. (Compare Figures 24 and 28.) In contrast, 
the two ring samples annealed at 500 C (Figures 27 
and 31) are in close agreement. It would seem that 
magnetic properties can be more easily reproduced in 
half-hard than in fully annealed samples of this ma¬ 
terial. 



Figure 21. Magnetization and permeability of Fe 
30%, Co 70%, reannealed and slowly cooled. 


A detailed series of measurements for determining 
the proper annealing temperature for half-hard 2\"- 
Permendur is shown in Figures 31A, 31B, and 32. It 
can be seen that the characteristics of the resulting 
material do not vary significantly if the annealing 
temperatures are in the range 450 to 625 C. For prac¬ 
tical purposes, annealing at 500 C, or even 450 C, is 
better than at higher temperatures since a larger coer¬ 
cive force is obtained. 

A compari.son between 2V-Permendur rings of 
varying thicknesses after a 450 C annealing is also 
shown in Figure 33. It will be seen that the various 
samples have the same coercive force but not quite 
the same remanence. 

A'icalloys 

The vicalloys were studied in the hope of finding a 
material comparable to 2V-Permendur but with a 
larger coercive force. The.se include the 8 per cent and 
6.5 per cent \Calloys, both of which can be precipita¬ 
tion-hardened by annealing at about 600 C for one 
or two hours. The major hysteresis loops of three 


.samples are shown in Figures 34 through 36. The co¬ 
ercive forces obtained in these samples are certainly 
of satisfactory magnitude. Unfortunately, none of 
the.se samples has large reversible permeabilitj' at the 
remanence point. 

The 6.5V-vicalloy scrolls are unsatisfactory in an¬ 
other respect. The peculiar shape of the demagneti¬ 
zation curves (Figure 35) shows immediately that the 
samples actually contain two phases, one of which 
has a coercive force of about 70 oersteds and the 
other (present in les.ser amount), a coercive force of 
30 to 35 oersteds. For this reason, if an a-c field is 
applied to the material at remanence, minor hystere¬ 
sis loops of large area will be traced out when the 
amplitude of the a-c field approaches 30 oersteds. 
This point is illustrated by the minor loops in the 
.same figures. Such loops in an actual transducer 
would cause excessive hysteresis los.ses (the small 
minor loop in Figure 36 corresponds to about 10 
watts per cc at 20 kc per sec) and distorted wave 
forms of the acoustic output. 

Further studies on another batch of 6.5V-vicalloy 
.sheets, which were also supplied b}^ BTL, show that 
the heterogeneous nature of the scroll samples is not 
inherent in the precipitation process. Thus the three 
hysteresis loops in Figure 37 are normal. Because of 
the sluggishness of the precipitation process, an in¬ 
crease in the time of annealing or in the annealing 
temperature pushes the coercive force to still higher 
^'alues. The reversible permeabilities at remanence of 
these three loops are also more than double tho.se of 
the scrolls. Unfortunately, all three .samples have 
rather small values of remanence .so that the increa.ses 
in reversible permeability do not represent any real 
improvement. Because of large hysteresis, the rema¬ 
nence will be reduced further under a large a-c field. 
This last point is illustrated by the minor loops in 
Figure 37. 

1.7.3 Static Measurements of 
Magnetostrietive Properties 

The re.sult.s of static measurements on the nickel 
and the 30% Fe, 70% Co rods are shown in Figures 
38 to 41. As previously noted, the observations were 
made by loading the .sample with weights of 100, 200, 
and 500 grams. The relation between the load and 
the change of magnetization was not quite linear, and 
along the steep portion of the normal curve there was 
also a hystere.sis effect which was rather pronounced 
in the case of the iron-cobalt sample. No attempt was 


CONFIDENTIAL 


















































80 


MAGNE;TIC and MAGNETOSTRICTIVE properties of IMATERIALS 




I 10 100 1000 


120 


100 


80 


60 ^ 


40 


20 


0 


H IN OERSTEDS 

Figure 22. A. Magnetization and penneahility of 0.006-in. 2V-Permendur strip in rolling direction, annealed. 
B. Magnetization and permeability of 0.006-in. 2V-Permendur strip in rolling direction, hard and annealed. 


made to study these effects in detail and only the re¬ 
versible ]3art of the change of magnetization with 
tension was recorded. The data presented for the 
nickel sample are those obtained with the 100-gram 
load, since both nonlinearity and hysteresis are small 
for this sample. For the iron-cobalt alloy, extrapola¬ 
tion to zero load has been carried out for each value 
of A. 


From equation (7c) we have the relation 



From this and the relation shown in (7a) we get the 
relation 

dirV/x' - 1 


CONFIDENTIAL 
















































































































































DISCUSSION OF RESULTS 


81 



Figure 23. Hysteresis in rolling direction of hard and annealed 2V-Permendur strip O.OOG in. thick. 



600 


500 


400 


300 ^ 


200 


100 


Figure 24. Magnetic properties of 2V-Pennendur as affected by annealing conditions. 


The curves A/a/m' — 1 vs \tvI are readily converted 
to curves of X and k vs 4x7, since E is practically con¬ 
stant with respect to varying values of 4x7. Taking 
2.2 X 10'^ for the value of E for both samples, the 
maximum values of X are —3.5 X 10^, and 1.(3 X 10^ 
for the nickel and the iron-cobalt samples respec¬ 


tively. The maximum values of k are 0.40 and 0.25. 
It will be seen later that the value 0.40 is the largest 
so far found for k. However, this is due to the unusu¬ 
ally high reversible permeabilities of the nickel rod 
rather than any abnormality in the values of X. 

The A/x/g' — 1 vs 4x7 curve of the iron-cobalt 


CONFIDENTIAL 
















































































































82 


MAGNETIC AND MAGNETOSTRICTIVE PROPERTIES OF MATERIALS 




I 10 100 1000 

H IN OERSTED'^ 


Figure 26. Magnetization and permeability of two samples of 2'V'-Permendur annealed 1 hour in liydrogen at 500 C. 


sample contains a number of irregularities which 
have not been observed in any other sample. How¬ 
ever, it is certain that these irregularities are not 


caused by errors in the measured values of p' since 
rather small variations of the field were used in de¬ 
termining p'. 


CONFIDENTIAL 













































































































DISCUSSION OF RESULTS 


83 


A further study of the data just presented will 
throw light on the phenomenon of magnetostriction. 
From ecjuation (Ga), 



ment of A. A similar situation exists when the area 
under the n' vs H curve is taken to determine the re- 
^’ersible portion of the magnetization. Thus, u.sing 
the data shown in Figures 6 and 21, we find: 

B'(rev) = 1,790, for 5'niax = 6,000 for nickel rod. 



H OEBSTEOS 

Figure 2S. Magnetization and permeaiiility of 2V- 
Permendur rings 0.006 in. thick annealed 1 hour in 
hydrogen at 500 C. 


respectively. By a slight transformation, equation (9) 
becomes 


(^) ^ _ 

\dB/p.T 4 x ( m ' — 1 ) 


( 12 ) 


In Figures 38 and 40, A is plotted as a function of 
//, and the total strain s for any value Hn of H is 
^iir times the area under the curve from H = 0 to 
H = //fl. Carrying out the integration graphically, 

.s = —16.1 X 10~® for nickel for H = 100, , 

6- = 26 X 10-'^for30%Fe, 70% Co for// = 100. ^ 

These values of s are much lower than those found by 
direct measurement of the quantity. However, the 
above values represent only the reversible parts of the 
fractional change in length, since mechanical hystere¬ 
sis is neglected both in the theory and in the measure¬ 


Therefore, the area under the curve of A/ (/r' — 1) vs 
B' will give 4x times the total fractional change of 
length for the maximum value of B'. The computed 
areas under the two curves give 

Stotai = —34.9 X 10'^ for nickel, /I'max = 6,000. 

Sto.ai = 63.7 X lO'-’ for 30% Fe, 70% Co, 

^'max = 20,000. 

Since the samples were not quite saturated, these cal¬ 
culated values of s are in good agreement with previ¬ 
ous observations. 


CONFIDENTIAL 







































































































































84 


MAGNETIC. AND MA(;NET(>STRICTIVE PROPERTIES OE MATERIALS 


Since it can be safely a.ssumed that the samples 
used in the HUSL experiments were comparable to 
those used by previous authors, the foregoing discus¬ 
sion leads to the conclusion that irreversible as well 
as reversible polarization contributes stresses in a 
clamped sample. This conclusion is of considerable 


eddy currents at the small d-c fields used in bridge 
measurements that it can be neglected. With this ap¬ 
proximation, the clamped-core reversible jiermeabil- 
ity M and the resistivity pe can be estimated from th(‘ 
clamped-core impedance and the dip angle 2j' of the 
resonance diameter of the motional impedance circle. 



H IN OERSTEDS 

Figure 30. Minor hy.stere.si.s loop, 2V-Perniendur 0.000 in. thick annealed for 2 hours in Ho at SOO t'. 


importance, since it implies that \dB' should be inte¬ 
grated in calculating the power output of a magneto- 
strictive transducer when it is driven by a large a-c 
field. 

4 . 7 . t Dynamic Measurements 

Cl.\mped-Core Imped,4.xce axd Related F.vctors 

The procedures for sei)aiating the clamped-core 
impedance and the motional impedance circle have 
already been de.scribed in Chapter 2, and earlier in 
the present chapter formulas have been summarized 
relating the fundamental coefficients p, X, E, and the 
various (piantities determined from the clamped-core 
impedance and the motional impedance or admit¬ 
tance circle. In the following paragraph complete sets 
of data will be set down and discu.ssed in order to 
show the degree to which experimental results agree 
with theory. 

complete analysis of impedance data, taking 
into account the effect of magnetic hysteresis, is 
somewhat comj)licated. Fortunately, the effect of hy.s- 
teresis is usually so small compared with the effect of 


In this way, p, Pe, and the eddy-current factors are 
determined; all the other quantities can be calculated 
b}' the formulas given in the last section. 

Owing to the variation of magnetic softness across 
the sheets'*- and perhaps to the imperfect insulation 
between the laminations, the A'alue of the resistivity 
thus obtained often appears erratic when compared 
with the directly measured value. In order to be cer¬ 
tain of the correctness of the eddy-cui’rent theory, an 
improved procedure is to obtain effective values of 
the resistivity Pe and the reversible permeability p by 
making use of all the values of the clami)ed-core im¬ 
pedance in the data. This involves (1) correcting the 
clamped-core imi)edance for leakage impedance, 
which can be estimated with fair accuracy and (2) 
plotting the clamped-core resistance against the 
clamped-core reactance. Since the corrected clamped- 
core impedance is proportional to the i)roduct of z- 
(the eddy-current jjarameter) ami x- the j^lotted 
points for various frequencies and various reversible 
]iermeabilities, corresponding to various magnetiza¬ 
tions, lie on a single locus that is similar to the one 
shown in Figure 3 of Chapter 3. The initial portion of 


CONFIDENTIAL 


































DISCUSSION OF RESULTS 


83 



Figure 31. A. Hysteresis, remanencc, and coercive 
force of 2V-Permendur annealed for 1 hour in hydrogen 
at different temperatures. H. Hysteresis, remanence, 
and coercive force of 2V-Permendur annealed for 1 hour 
in hydrogen at different temperatures. 


the locus, then, is an arc of a circle of which the 
radius is 


r = 1.5 X 


2N'Hbp. 

-, 

raf 


(13) 


where t is the thickness of the laminations, pe the re¬ 
sistivity, and other fiuantities are as defined in the 
previous section. Since all the ciuantities except pe in 
the last expression are known, it is a simple matter to 
find the radius from the locus and evaluate Pe- 

Next, a point is located on the horizontal diameter 
of the circle that is at a distance ecjual to two-thirds 
the radius to the right of the center. B}" using this 
point as a pole and projecting the points on the initial 



Figure 32. Remanent magnetization and coercive 
force of hydrogen-annealed 2V-Permendur sheets 0.006 
in. thick, a.s function of ambient temperature. 



Figure 33. Hysteresis of 2V-Permendui' rings of vary¬ 
ing thickness annealed at 450 C. 

portion of the locus onto the vertical axis, the inter¬ 
cepts thus obtained will be equal to 

oiLo = -’ 

a 

whei-e values of Lo are the clamped-core inductances 
free from eddy-current effect. Knowing the frequency, 
the values of p can again be independently calculated. 

The procedure just described is illustrated in Figure 
42 by the data for the soft-annealed 2V-Permendur 
ring stack which will be discussed presently. The val- 


CONFIDENTIAL 




























































































































































































86 


ma(;netic and magnetostrictive properties oe materials 



Figure 34. I ly-steresis of 8V-vicalloy laminatioiis 
0.014 ill. thick. 



■100 0 100 


H IN OERSTEDS 

Figure 3o. Scroll of 6..5-vicalloy 0.002 in. thick, 
annealed 2 hour.s at GOd C. 

lies plotted in this case are the clamped-core imped¬ 
ances at resonance for various polarizing fields and 
hence for various reversible permeabilities, neglecting 
small differences in the resonant frequency. Since the 
copper resistance of the winding and the leakage im- 
liedance are constant, it is not necessary to correct 
the clamped-core impedance before plotting. Instead, 
the corrections are determined by the location of the 
circle. 

Four complete sets of data are shown in Tables 2 
to 5 for soft-annealed A-nickel, 45-Permalloy, 2^’-Per- 
mendur, and half-hard A-nickel. The 2^"-Permendur 
sample is the one from which the curve of Figure 42 
was derived. The measurements were made with the 



-100 0 100 
H IN OERSTEDS 


Figure 36. Effect of two pha.ses in 6.5-vicnlloy on 
minor hysteresis loojis at remanence. 



Figure 37. Hystere.sis curves for 6..5-vicalloy for 
different anneafs. 


samples polarized to various intensities la by various 
d-c fields //q. In accordance with the usual jiractice, 
the values of la were obtained along the normal curve 
for soft sainjiles and along the demagnetizing branch 
of a major hysteresis loop for half-hard or hard sam¬ 
ples. The upper columns of each table give an overall 
check of the eddy-current theory and the lower col¬ 
umns the values of the important ipiantities deter¬ 
mined from the motional imjtedance circle and those 


COXFIDENTIAL 




































































































































































DISCUSSION OF RESULTS 


87 


of the electromechanical coupling coefficient k, etc., 
calculated therefrom. 

The quantities listed in the upper columns of 
Tables 2 to 5 are defined as follows: 

(u' = reversible permeability obtained from magnetic 
measurements, 

= dip angle of the resonance diameter of motional 
impedance circle equal to twice the eddy-cur¬ 
rent loss angle, neglecting hysteresis, 

Rc + jXc = corrected clamped-core impedance obtained by 
interpolation from clamped-core impedance 
curves, 

fi = reversible permeability computed by the method 
just described. 



Figure 38. Nickel rod annealed 1 hour at 1000 C in 
hydrogen. 



0 1000 2000 3000 4000 5000 6000 

4Tn 


Figure 39. Nickel rod, annealed 1 hour at 1000 C' in 
hydrogen and slowly cooled. 

The value of fi and the simultaneously determined 
\’alue of the resistivity are, in turn, used to calculate 
j", Rc, and by the formulas of eddy-current theory. 
These calculated values pro\ ifle a check on the con¬ 


sistency of the series of analyses and are shown in the 
last three upper columns in each table. 

In earlier discussions, emphasis has been placed on 
the difference in meaning of p' and p. As can be seen 
from equation (7a), the numerical difference be¬ 
tween the two is practically equal to the square of the 
electromechanical coupling coefficient k. In the cases 
of the soft-annealed A-nickel and 45-Permalloy sam- 
Iiles of Tables 2 and 3, the values of p do seem to lie 
smaller than the corresponding values of p', but in 
general the pairs of values fail to show consistently 
the existence of the electromechanical coupling co¬ 
efficient. In the case of the Permendur sample, the 



Figure 40. Iron-cob:dt rod annealed 1 hour at 1000 C 
in hydrogen and slowly cooled. 


data only show that p' and p are of the same order of 
magnitude. The discrepancy between experiment and 
theory is due mainly to the large errors in the graph¬ 
ically determined values of p, and to some extent to 
errors in the polarizing field. (The meters used to 
measure the polarizing currents during the course of 
impedance measurements wei’e not so accurate as 
those used for magnetic mea.surements.) 

The agreement between the observed and calcu¬ 
lated values of f and Ac in the tables is generally 
good. Large discrepancies are present, however, in the 
case of Rc. This is largely due to the fact that Rc can¬ 
not be interpolated as accurately as Ac. Also, for 
small total re.sistances, the dissipations in the con¬ 
densers used in the briilge cause .some errors in Rc. 

For the half-hard A-nickel sample, there is no need 
to evaluate p, since the values of k are small for this 
sample. Accordingly, the measured values of p' and 
p have been used to calculate the theoretical values of 
t, Rc, and A'c in checking the theory. Table 5 shows 
the agreement in this case to be excellent. 

From the above discu.ssions it can lie concluded 
that the eddy-current theory is on the whole fairly 


CONFIDENTIAL 





































































































































MAGNETIC AND MAGNETOSTRICTIVE PROPERTIES OF MATERIALS 


KK 


Table 2. Measurements for soft-annealed A-nickel (0.005 in.). Test conditions: 1 hr at 1000 C in H 2 ; 
50 laminations; Vinylseal consolidated; OD, 3.31 in.; ID, 2.65 in.; turns of winding, 336. 


//o 

4Tr/o 

f 

f 

Rc 

A'c 


fcalc 

Rc calc 

Ac calc 

oersteil 

gausses 

M 

degrees 

ohms 

ohms 

M 

degrees 

ohms 

ohms 

3.0 

2520 

137 

24.6 

183 

449 

122 

21.3 

1.56 

399 

5.0 

3105 

10.5 

20.3 

119 

370 

98.5 

17.8 

109 

340 

7.1 

3530 

84 

15.8 

78.8 

302 

81.5 

15.0 

79.0 

291 

10.0 

3930 

66.0 

14.4 

59.3 

272 

69.4 

12.7 

.58.1 

2.53 

14.1 

433.5 

.50.7 

9.6 

24.1 

197 

4,8.1 

9.2 

28.6 

181 

19.6 

46.S0 

39 

7.7 

14.6 

166 

38.4 

7.4 

18.4 

146 

30.3 

.5110 

26 

4.2 

6.6 

102 

25.5 

5.0 

8.5 

98.3 

//o 

oersted 

fr 

kc sec 

D 

ohms 

Q 

k 

A'-10->2 
dynes cm^ 

dynes 'cm^ 

-xio-‘ 

dynes 'gauss cm- 

R’m 

R„, 

Pot eff 

3.0 

19.58 

1015 

30.1 

0.272 

1.92 

2.04 

0.94 

0.86 

0.75 

5.0 

19.48 

1023 

28.6 

0.304 

1.90 

2.06 

1.20 

0.88 

0.80 

7.1 

19.46 

1027 

32.4 

0.312 

1.90 

2.08 

1.39 

0.88 

0.83 

10.0 

19.46 

1032 

36.3 

0.310 

1.90 

2.08 

1 ..55 

0.86 

0.84 

14.1 

19.53 

1080 

.52.0 

0.310 

1.91 

2.10 

1.78 

0.95 

0.93 

19.6 

19.64 

1120 

78.6 

0.282 

1.93 

2.10 

1.85 



30.3 

19.83 

1133 

142 

0.271 

1.97 

2.13 

2.18 

0.98 

0.98 


T.able 3. Measurements for soft-annealed 45-Permalloy (0.005 in.). Test conditions: 1 hr at 1000 C in dry H.; 
.50 laminations; Vinylseal consolidated; OD, 3.31 in.; ID, 2.65 in.; turns of winding, 296. 


oersted 

4n-/o 

gausses 

/ 

M 

r 

degrees 

Rc 

ohms 

Ac 

ohms 

M 

Tcalc 

degrees 

Rc calc 
ohms 

A"c calc 

ohms 

2.9 

11,960 

375 

7.0 

90 

104.5 

396 

7.6 

140 

1060 

4.9 

12,770 

24.5 

4.7 

37 

670 

244 

4.7 

.54.2 

664 

9.7 

13,830 

131 

3.2 

13.7 

367 

121 

2.4 

13.8 

335 

15.5 

14,420 

70 

0 

6.7 

193 

65 

1.3 

4.21 

183 

23.3 

14.790 

32 

1.8 

2.3 

83 

28.5 

0.65 

0.88 

82 

38.9 

15,020 

9.4 

0.5 

0.89 

26.2 

9.6 

0.3 

0.134 

28 


He 

oersted 

fr 

kc sec 

D 

oil ms 

Q 

k 

£-'.10-12 
dynes /cm- 

AlO-'^ 
dynes/cm^ 

-xio-^ 

dynes gauss cmi^ 

Pot eff 

2.9 

17.15 

6200 

81.7 

0.259 

1.37 

1.47 

0.45 

0.87 

4.9 

17.17 

.5900 

99.2 

0.287 

1.37 

1.49 

0.63 

0.91 

9.7 

17.36 

5250 

174 

0.288 

1.40 

1..53 

0.91 

0.94 

15.5 

17.63 

3800 

31.5 

0.249 

1.45 

1.55 

1.08 

0.9.5 

23.3 

17.936 

1345 

478 

0.182 

1..50 

1.55 

1.20 

0.96 

38.9 

18.190 

193.5 

1040 

0.082 

1..54 

1.5.5 

0.93 

0.95 


satisfactory and that the assumption of negligiljle 
hysteresis effect is justified. 

In the lower columns of Tables 2 to .o, fr and D are 
accurate to within 1 per cent. The precision to which 
Q is determined depends upon the magnitude of Q, 
but in general the error is not greater than 5 per cent. 
The interpolated values of are jn’ecise to about the 
same degree. Therefore k should generally be precise 
to about 0 per cent. Bocau.se of the high accuracy of 
fr and the small magnitude of k-, both E' and E have 
high relative accuracy. On the other hand, the values 


of X may have errors considerabl}' higher than .5 per 
cent, becau.se, in determining these values, the values 
used for/:/were thosededucedfromeddy-currenttheory. 

The ratio of that part of motional resistance. 
which is due to edd.v-current effect to the total mo¬ 
tional resistance R,„, and the potential efficiency given 
in Tables 2, .3, and 5 ha\-e no bearing on the determi¬ 
nation of the fundamental coefficients. The actual 
values of these (luantities merely indicate that highly 
efficient transducers can be realizefl by reducing ex¬ 
ternal mechanical resistances. 


CONFIDENTIAL 























































DISCUSSION OF RESULTS 


89 


Table 4. Measurements for soft-aimealed 2V-Perinendur (0.006 in.). Te.st conditions: 2 hr at 800 C in H-.; 
40 laminations; Vinylseal consolidated; OD, 2.86 in.; ID, 2.42 in.; turns of winding, 162. 


Ho 

oersted 

47r/o 

gausses 

3.6 

11,400 

6.9 

13,370 

12.8 

15,190 

25.2 

17,230 

46.6 

19,070 

66.5 

20,010 


r 

M 

r 

degree.s 

325 

26.7 

247 

22.4 

178 

16.6 

110 

10.3 

60.5 

4.5 

38 

4.4 


Rc 

ohms 

A4 

ohm.s 

102 

195 

72 

171 

40 

134 

16 

85.0 

4.7 

45.4 

2.4 

31.3 


fcalc 

degrees 


327 

26.7 

260 

22.0 

187 

16.5 

112 

10.5 

57.6 

5.4 

39 

3.7 


Rc calc A’c calc 

ohms ohms 


99 

198 

69.6 

172 

40.1 

134 

15.6 

85.5 

4.34 

45.9 

2.1 

31.8 


Ho 

oersted 

fr 

kc/sec 

D 

ohms 

Q 

k 

£’'•10-12 
dynes/cm^ 

E-10-12 
dynes ! em^ 

-xio-i 

dynes/giiuss cm^ 

3.6 

23.50 

390 

42.0 

0.220 

2.01 

2.09 

0.49 

6.9 

23.40 

422 

32.1 

0.274 

1.99 

2.12 

0.72 

12.8 

23.34 

432 

34.8 

0.294 

1.98 

2.15 

0.91 

25.2 

23.48 

422 

53.4 

0.292 

2.01 

2.19 

1.16 

46.6 

23.78 

265 

79.3 

0.261 

2.06 

2.21 

1.41 

66.5 

24.12 

267 

156 

0.227 

2.11 

2.23 

1.55 


Table 5. Measurements for half-hard A-nickel (0.005 in.). Test conditions: 1 hr at 600 C in Ho; 
50 laminations; Vinylseal consolidated; OD, 3.31 in.; ID, 2.65 in.; turns of winding, 339. 


Ho 

47r/o 


f 

Rc 

A'c 

fcalc 

Rc calc 

A c pale 

oersted 

gausses 

t 

degrees 

ohms 

ohms 

degrees 

ohms 

ohms 

-15.6 

2490 

23.0 

2.55 

5.23 

92.4 

2.90 

4.74 

96.0 

0 

3280 

19.5 

2.55 

4.23 

80.9 

2.46 

3.45 

81.3 

27.0 

3975 

14.7 

1.8 

2.63 

61.9 

1.82 

1.95 

61.3 

61 

4450 

10.8 

1.1 

2.02 

46.9 

1.3 

1.04 

44.6 

110 

4890 

7.8 

0.95 

1.29 

32.5 

1.0 

0.57 

32.6 

Ho 

fr 

D 

Q 

k 

£'•10-12 

£•10-12 

-\-io-i 


oersted 

kc/sec 

ohms 

dynes/cm- 

dynes / cm^ 

dynes/giiuss cm2 

Pot eff 

-15.6 

20.64 

859 

898 

0.099 

2.16 

2.19 

0.86 

0.91 

0 

20.61 

1080 

711 

0.140 

2.16 

2.20 

1.32 

0.93 

27.0 

20.57 

1064 

761 

0.149 

2.15 

2.20 

1.63 

0.94 

61 

20.49 

1146 

1078 

0.152 

2.13 

2.18 

1.94 

0.96 

no 

20.64 

943 

1453 

0.140 

2.17 

2.21 

2.10 

0.97 


The jMagnetostrictive Constant and the 
Coefficient of Electromechanical Coupling 

^'alues of X and k obtained liy dynamic measure¬ 
ments on various samples, including; those of Tables 
2 to 5, are plotted as function.s of the intensity of 
polarization in Figures 43 to 48. The values of X for 
the nickel rod as deduced from the values of A V' — 1 
in Figure 39 are also shown in Figure 43 foi- purposes 
of comparison. Figures 43 and 44 also contain the re¬ 
sults obtained at 22 and 48 C from sample No. 1 of 
the 10-mil oxide-annealed A-nickel sheets of Figure 7. 
These latter results are part of a series to be discussed 
in some detail at the end of this chapter. 


For hydrogen-annealed nickel, the fair agreement 
between the X vs 47r/ curve obtained by static meas¬ 
urements and that obtained by dynamic measure¬ 
ments tends to confirm the correctness of the thermo¬ 
dynamic relations as well as the transducer theory. 
However, differences definitely exist among the X vs 
47r/ curves of the variously treated A-nickel samples. 
Since the longitudinal magnetostriction in single 
nickel crystals is anisotropic, such differences can be 
expected if, in the polycrystalline samples, perfect 
random orientations of the grains are not always ob¬ 
tained. On the other hand, it is not clear whether 
internal stresses in the samples can also affect the 
magnitude of X. 


CONFIDENTIAL 






























































90 


MAGNETIC AND MAGNT:TOSTRICnVE I'KOPERTIES OF MATERIALS 



Figure 41. Iroii-cohalt I'od annealed 1 hour at 1000 C in liydrogen and slowly cooled. 


5 

< 



Figure 42. Locus of clamped-core impedance at resonance of O.OOO-in. 2V-Permendur ring stack annealed for 2 hours 
in hydrogen at 800 C. 


It i.s not known whether the saturation magnetiza¬ 
tion of Z-nickel is considerably smaller than that of 
A-nickel. On the basis of Figure 43, annealed Z-nickel 
has about the .same values of X as oxide-annealed 
A-nickel. Becau.se of the small reversible permeabil¬ 


ities of the particular sample chosen for dynamic 
measurements, the values of k shown in Figure 44 for 
Z-nickel appear rather small. Actually, the aged 
Z-nickel sample of Figure 13 shows considerably 
larger reversible permeabilities and therefore is ex- 


COXFIDEXTIAL 













































































































































DISCUSSION OF RESULTS 


91 


pecteil to ha\’e as large k values as oxide-annealed 
A-nickel, although the maximum value of k comes at 
a higher field intensity. In view of its higher resistiv¬ 
ity and superior mechanical properties, the Z-nickel 
may yet prove superior to A-nickel. 

1 he results obtained from D-nickel are interesting 
but rather disappointing. As may be seen from Figure 
43, the 5 per cent of dis.solved manganese has reduced 












































• .0 

D5 IN 

A Nl 

CKEL 

ANNE 

aled 

IN H 


000 

c 





oiHt bAME ANNEALED AT 600C 
t OXIDE annealed 

UNANNEALEO AS RECEIVED 

O.OlO IN OXIDE annealed. MEASURED AT 48 C 

V THE SAME MEASURED AT 22 C 













i 






it 












0 


e 

C / 












X 

r 












X , 

/ V 














































-- 





























1 










A 


















, 

^ - 














0 1000 2000 3000 4000 5000 6000 

B' 


Figure 43. Magnetostrictive coefficients 


Table 6. Dynamic measurements at remanence. 



Br 

r 

k 

X 

6.5V-vic;illoy 
scroll No. 1 

13,7.50 

13 

0.082 

1.01 X io< 

8V'-vicalloy 
ring stack 

11,180 

15.3 

0.080 

0.93 X 10^ 



the value of X in nickel at high inductions by more 
than 50 per cent. This was the only case investigated 
in which nickel was alloyed with a considerable per¬ 
centage of a nonmagnetic element. 

Further experiments on nickel with small additions 
of other elements might well be made. 

INIeasurements on the X'icalloys 

Only two sets of dynamic measurements have been 
made on the vicalloys. The results of these measure¬ 
ments are shown in Table fi. 

In the foregoing discussions no mention has been 
made of the value of the resistivity as derived from 
impedance data by applying eddy-current theory. 
Using the actual thickness of the laminations, the de¬ 
rived value of the resistivity departs considerably 
from the measured ^’alue in many cases and therefore 


deserves particular attention. A comparison of the 
values of resistivity derived from impedance data 
with those directly measured is shown in Table 7, 
in which the values of density p„, and of Young’s 
moduli E' and E are also listed. 

The measured values of the resistivity are shown 
in the third column of Table 7. These values are only 
accurate to within 1 to 3 per cent in absolute magni¬ 
tude becau.se of the small thicknesses of the samples, 
but their relative accuracy is about 1 per cent. For 
A-nickel, the small differences in the several values 
can be explained by the differences in the amount of 
cold work remaining in the variously treated samples. 
The large influence of heat treatment on the resis¬ 
tivity is, of course, expected in the vicalloys, since in 
these cases a i)artial phase transformation is involved. 
The considerable differences among the values ob- 


COXFIDENTIAL 




























































































































92 


MAGNETIC AM) MA(;NETOSTRIGTIVE PROPERTIES OE MATERIALS 


tained on 2\'-Permendur indicate that even in this 
lo\v-\’anadiiim alloy the phase transformation is not 
always complete; yet it is still not clear why, in this 
case, the heat treatment tends to change the resis¬ 
tivity in the direction opposite to that observed foi' 
the vicalloys. 



1000 2000 3000 4000 5000 6000 

B' 

Figure 44. Electromechanical coupling coefficients 
of sample.s of nickel a.s function of B'. 

The fourth column of Table 7 shows the values of 
resistivity derived from impedance data. Among 
these values a few are enclosed in parentheses because 
the}" were obtained by the method illustrated in 
Figure 42. With the exception of a few samples, the 
value of the resistivity that fits impedance data is 
seen to be 15 to 40 per cent smaller than the mea.s- 
ured value. As there is no consistency in these dis¬ 
crepancies, the most plausible explanation for them is 



0 ' 


Figure 45. Magnetostrictive coefficient of hydrogen 
annealed 4.5-Permalloy a.s function of B' (Bell Tele¬ 
phone Lahoratorie.s, Inc.). 



B' 


Figure 40. Electromechanical coupling coefficient of 
4,5-Permalloy (Bell). 


CONFIDENTIAL 






































































































































DISt:USSION OF KFSULTS 




Table 7. A comparison of resistivity, density, and Young’s modulus of magnetostrictive materials under 
various conditions. Values enclosed in parentheses were obtained by the method illustrated in Figure 42. 


Material 

Treatment 

oba 

ohm-cin 

calc 

ohm-cni 

Pm 

grams/cc 

E'- 

dynes /cm- 

E- 

dynes/cnp 

A-niekel 

5-mil, unannealed 

10.4 10-« 

10.4 lO-® 

8.9 

2.16-10'2 

2.17-10'2 

A-nickel 

5-mil, o.xide-annealed 

10.0 

(7.2) 

8.9 

2.05 


A-nickel 

10-mil, oxide-annealed 

9.1 

9.1 

8.9 

1.99 

2.15 

A-nickel 

5-mil, 1 hr at 1000 C in H> 

9.4 

(6.2) 

8.9 

1.90 

2.08 

.\-nickel 

5-mil, 1 hr at 600 C in Hj 


10.0 

8.9 

2.16 

2.20 

Z-nickel 

14-mil, annealed, quenched, aged 

14.3 


8.86 



Z-nickel 

annealed, quenched 


14.3 

8.86 

2.06 

2.13 

D-nickel 

20-mil, unannealed 

20.5 


8.79 



D-nickel 

1 hr at 1000 C in H,, 


15.0 

8.79 

2.06 

2.11 

45-Permalloy 

unannealed 

54.4 


8.16 



45-Permalloy 

1 hr at 1000 C in drv H. 


(53.9) 

8.16 

1.40 

1.53 

2V-Permendur 

2 hr at 800 C in H 2 

38.9 

30.2; 26; 

8.18 

1.98 

2.15 



39.4 

29.8; (24) 




2V-Permendur 

1 hr at 500 C in H., 

35.4 

28.8; 33.5; 

8.18 

2.26 

2.36 




28.2 




2V-Permendur 

unannealed 

31.1 


8.18 



6.5V-vicalloy 

unannealed 

89.9 





6.5V-vicalloy 

1 hr at 600 C in Ho 

71.3 


8.1 

2.46 

2.48 

8V-vicalloy 

unannealed 

90.1 





8V-vicalloy 

2 hr at 600 C in H-, 

60.3 

53.8 

7.75 

2.22 

2.24 




0 I0J300 20,000 

B' 


Figure 47. Magnetostrictive coefficients of various 
samples of 2V-Permendur. 


Figure 48. Electromechanical coupling coefficients 
of samples of 2V-Permendur. 


CONFIDENTIAL 




























































































































9i 


MAGNKTIC AND MAGNETOSTRICTIVE 1‘ROPEKTIES OF MATERIALS 


the nonuniformity of the reversible permeability 
across the sheet or on occasional improper consolida¬ 
tion. 

In Table 7, the values of p„, are either taken from 
jrrevious authors or determined by weighing. The 
\’alues of E' for the soft-annealed samples are actu¬ 
ally the minimum values approximately correspond¬ 
ing to the maximum values of k. Those for the half- 
hard and hard samples are taken at the remanence 
iroint. It might be remarked again that E' is the 
Young’s modulus to be used in calculating the actual 
velocity of .sound in the material. 



It should be pointed out that the steady increa.se of 
Young’s modulus E with increasing B' in the cases of 
the .soft-annealed materials and the falling-off of X 
after it has reached a maximum in the cases of 
D-nickel and 45-Permalloy are phenomena that are 
not very well understood. 

Significance of Result.s for Transducer Design 

Some comparison of the various materials can now 

be made from the standpoint of transducer design. As 

can be seen from equations (28) and (83) of Chapter 

3 the open-circuit sensitivity of a magneto,strictive 

transducer operated as a receiver below resonance is 

approximateh^ proportional to Xg. The open-circuit 

sensitivity for a given total impedance is, however, 
/“ 

jiroportional to XVg or the electromechanical-cou¬ 
pling coefficient k. Also, as discussed in Chapter 3, the 
po.ssible width of response of a transducer operating 
at resonance is approximately projiortional to k. 
Although the increase of X and the decrease of g 



Figure .50. Variation under alternating field of half- 
hard ring lamination.s 0.006 in. thick, annealed at 



hdouRE .51. Illustrating joint effect of field and stre.ss 
variation on magnetization. 


with increasing intensity of polarization make the 
theoretical efficiency higher at higher intensities of 
polarization, it is desirable to operate the transducer 


CONFIDENTIAL 




















































DISCUSSION OF KESULTS 


95 


at the maximum value of k. For, as the electro¬ 
mechanical coupling; decreases, the impedance be¬ 
comes quite small, and copper losses and leakage flux 
will play an ever increasing part in determining the 
efficiency. For these reasons, the most important 
single quantity that can be u.sed as a criterion of the 
magnetostrictive material is the maximum value of 
the coefficient of electromechanical coupling. 

A second ciuantity of importance is the depth d, 
characteristic of the penetration of the magnetic field 
into the material. According to equation (1) of Chap¬ 
ter 3,d is proportional to the square root of the ratio 
of the resistivity, pe to the reversible permeability p. 
The thickness |of the sheets which can be used for 
specified eddy-current losses is proportional to d. 
Thus, when other factors remain the same, a high 
value of "s/pf p allows thicker laminations to be used, 
with conseciuent reductions in manufacturing cost 
and difficulty of construction. 

Numerical values of the quantities under discussion 

Table 8. A quantitative compari.son of materiats used 
in transducer design. Values used are from the data 
plotted in Figures 6 to 49 and the measured values of 
n' and p,. 


At Optimum Polarization 


Material 

Tre.atment 

A'max 

m' 

v'p,/m'X103 

5-mil A-nickel 

1 hr at 

1000 C in H.. 

0.315 

70 

0.38 

5-mil A-nickel 

oxide- 

annealed 

0.240 

30 

0.58 

10-mil A-nickel 

oxide- 

annealed 

> 0.32 

> 60 

< 0.41 

20-mil D-nickel 

1 hr at 

1000 C in H. 

0.286 

100 

0.45 

5-mil 45- 
Permalloy 

1 hr at 

1000 C in H, 

0.298 

195 

0..53 

6-mil 2V- 
Permendur 

2 hr at 

800 C in 

0.296 

150 

0.51 

5-mil A-nickel 

1 hr at 600 C 

0.152 

12 

0.91 


At Remanence 


Material 

Treatment 

k 



5-mil A-nickel 

1 hr at 600 C 

0.14 

19 

0.72 

6-mil 2V- 
Permendur 

1 hr at 

500 C in Hj 

0.204 

54 

0.85 


are reproduced for several materials in Table 8. Hy¬ 
drogen-annealed 5-mil A-nickel and oxide-annealed 
10-mil A-nickel are seen to be superior to the other 


materials in respect to but are inferior from the 
standpoint of N/p, p. O.xide-annealed 5-mil A-nickel 
is inferior to Permalloy and Permendur with regard 
fo /c^ax) but the three are almost equivalent in 
n/P f/ p. It is to be noted that a higher value of kmxx 
may be achieved for oxide-annealed 5-mil A-nickel by 
increasing the annealing temperature or time. The 
value of fcniax of annealed D-nickel is comparable to 
that of A-nickel, but the corresponding value of 
Vpjp is not large. It will also be noted that D-nickel 
and Permalloy are somewhat more critical with re¬ 
spect to polarizing flux than nickel, as shown by the 
k vs AttI curve in Figures 44 and 46. Annealed 
Z-nickel has not been included in Table 8 because the 
small amount of information obtained on this ma¬ 
terial was not conclusive. 

The cost of Permendur sheets and of 45-Permalloy 
is very much greater than that of nickel. Further¬ 
more, both these alloys ha\'e to be heat-treated in 
a reducing atmosphere, whereas the oxide coating 
formed on nickel by air annealing is a good insulator 
which obviates any extra precautions to prevent elec¬ 
tric contact between laminations. For general use 
nickel is therefore believed to be superior, on the 
whole, to the two alloys. 

The rather small value of the k of half-hard nickel 
at remanence, shown in Table 8, already indicates 
that nickel is inferior to Permendur for operation at 
remanence. But for this latter purpose other factors, 
to be discussed in the next section, must also be 
taken into account. 

For transducers to be u.sed at high levels, the maxi¬ 
mum power output must be taken into consideration. 
Because of the complicated nature of the problem, 
only the maximum stresses that can be practicably 
set up in the materials by magnetostriction will be 
indicated. These can be obtained by integrating the 
areas under the X vs 47r/ curves. From Figures 43, 
45, and 47, we find: 

= 6.000 = 70 X 10'* dynes per sq cm for 
A-nickel, 

Pb- = i 5 ,ono = 40 X HP dynes per sq cm for 4.5- 
Permalloy, 

Pg- = 20.000 = 105 X lO"' (ijmes per sq cm for 2V- 
Permendur. 

Permendur would accordingly seem to be superior 
to the other materials in this respect. 


CONFIDENTIAL 




























96 


MACiNETIC AND IMAGNETOSTKICTIVE PROPERTIES OF MATERIALS 



Figure 52. Variation of normal magnetization of o.xide-annealed A-nickel, with temperature for small values of H. 


4.8 TRANSDUCERS OPERATED AT 
REMANENCE 

The half-hard materials used in transducers oper¬ 
ated at remanence have, in general, large magnetic 
hysteresis. Once the active material of such a trans¬ 
ducer is demagnetized its remanence will remain 
small. Demagnetization results from the application 
of too large an a-c field as well as from severe strains 


or mechanical vibrations. This section will first de- 
scril)e some experimentally obtained data from 
which it is possible to estimate the maximum a-c field 
that can be used for a given material from its major 
hysteresis loop. The demagnetizing effect of mechan¬ 
ical vibrations will then be qualitatively explained. 
The maximum magnetostrictive stresses to be ob¬ 
tained in half-hard A-nickel and Permendur will be 
estimated and .some experimental tests describeil. 


CONFIDENTIAL 





















































TRANSDUCERS OPERATED AT REMANENCE 


97 



H IN OERSTEDS 

Figure 53. Variation of normal magnetizaticm of oxide-annealed A-nickel, with temperature for higher values of H. 


4 . 8.1 Some General Rules about 
]VIinor Hysteresis Loops 

Sui^pose the material is magnetized by a d-c field 
whic'h can bo slowly increased, decreased, or re- 
\'ersed. Any variation of the field will trace out a 
path in the B vs H plane. A number of tests and 
measurements show that the following I'ules hold. 


When the field is increased to .such an extent that 
point 1 {Hi, Bi) is reached, magnetization will not in 
general retrace the original path when the field de¬ 
creases (Figure 49). Subsequently, if the field re¬ 
verses on reaching point 2 {H 2 , B 2 ), the succeeding 
path will again be different from that used in going 
from 1 to 2 but will reach point 1 if the field does in¬ 
crease to the value Hi. 


CONFIDENTIAL 




















































9K 


MAGNETIC AND MAIiNETOSTKICTIVE IMIOPERTIES OE MATERIALS 


If, on reaching point 1 the second time, the field 
turns to decrease again, the j^ath followed in going 
from 1 to 2 the first time will be retraced. Similarly 
if, on reaching point 2 the second time, the field turns 
from decreasing to increasing again, the path fol¬ 
lowed in going from 2 to 1 the first time will also he 
retraced. Thus a minor loop is stabilized by a com¬ 
plete cycle of variation of the field from Hi to H<i and 
back to Hi. 



oxide-annealed A-nickel, with temperature for .small 

values f)f H. 

If, in an intermediate stage, the field does not turn 
to decrease on reaching point 1 but continues to in¬ 
crease, the path traced out will be the continuation 
of the original path, as if the minor loop had not been 
traced. 

The same holds true if point 1 is reached not by 
an increasing but by a decreasing field. 

These rules are illustrated schematically in Figure 
49. It will be noticed that the above rules are merely 
a generalization of Rayleigh’s law described pre\'i- 
ously. With these rules the following inferences can 
be drawn: 

1. All minor loops are wholly enclosed by the 
major loop obtained by revensals of a field that is 
strong enough to saturate the material. 

2. Successive applications to the material of a field 
which varies cyclically between the extreme values 
Hi and Hi will retrace the same minor loop no matter 
at what point of a cycle the fiekl is removed after each 
application. 

3. If a field varying cyclically between the ex¬ 
treme values Hi and //o is first applied to the material 


to trace out a primary minor loop, .sid^sequent arbi¬ 
trary variations of the field within the range Hi to 
Hi will trace out secondary minor loops that are 
wholly enclosed by the primary minor loo]). 

The half-hard A-nickel sample of Figure 16 may be 
taken as an example. The descending branch of the 
major hystere.sis loop and four minor loops are repro¬ 
duced in Figure 50. Minor loops 1 and 2 were ob¬ 
tained by a cyclically varying field of + 15.4 oersteds 
and +22.7 oersteds respectively, the initial magneti¬ 
zation being the rententivity marked by A. Loops 3 
and 4 were obtained by cyclically varying the field 
between +15.4 and — 15.4 oersteds, starting from the 
remanences B and C respectively. In obtaining the.se 
minor loops, the field can start to change either in the 
positive or in the negative direction, in accordance 
with the rules given above. 

If the rules applied strictly, loop 1 .shouhl have its 
lower tip on the major loop and loop 4 should have its 
upper tip on loop 2. Failure in this respect is due to 
oKservational errors, fluctuations of the field, and 
transient mechanical vibrations. 

The effect on a .sample of an a-c field of low fre- 
(picncy .should be the same as that of cyclically vary¬ 
ing a d-c fiekl. Thus an a-c fiekl of amplitude 22.7 
oersteds, when applied to the nickel sample of Figure 
50, will also trace out the minor loop 2. However, an 
a-c fiekl cannot be controlled with the same accuracy 
as a d-c fiekl. After removing the a-c fiekl, therefore, 
the remanence may be at any point on the line BC. 
depending on the exact j)oint of a cycle at which the 
a-c fiekl is removed. This point should l)e remem¬ 
bered, as it often causes confusion in certain types of 
magnetic experiments. 


1 . 8.2 Demagnetization Effeet of 
Strains 

The foregoing discussions are based on the assum])- 
tion that the sample is in static eciuilibrium. In the 
actual case of a transducer driven at resonance, the 
active material is alternately strained by the vibra¬ 
tions of the transducer. The strain amplitude is pro¬ 
portional to the mechanical Q, as well as to the 
amplitude of the exciting magnetostrictive stress, so 
that it can be much larger than the natural change of 
length arising from magnetostriction. Since lyvsteresis 
is something inherent in the material, changes of 
magnetization caused by strains are also partly irre- 
vensible. When a transducer polarized at retenti\'ity 


CONFIDENTIAL 

































































TRANSDUCERS OPERATED AT REMANENCE 


99 


is first set into vibration l)y an a-o field, the phase re¬ 
lations between the transient vibrations and the field 
are somewhat complicated. In any case, during part 
of the first few cycles, a demagnetizing field is aided 
by a demagnetizing strain, so that the total demag¬ 
netization is actually larger than that estimated from 
measurements of the type shown in Figure 50. 

The joint effect of a fiekl and a stress on magnetiza¬ 
tion is further (lualitatively elucidated in Figure 51, 


will not return to state Bo after removal of the tension 
and the field but will go along part of a minor loop 
to Bq. The sample is therefore demagnetized by an 
amount Bo — B'q. If at some instant the transients 
set u]) by a sudden application of an a-c field on a 
transducer bring the active material to some such 
state as C, the transducer will be demagnetized by 
about the same amount. 

It is clear from the foregoing that the recpiirement 



H IN OERSTEDS 

Figure 55. Wnriation in reversible permeability of oxide-annealed .4-nickel, with temperature for higher values of H. 


which shows the descending branches of the major 
hysteresis loops of a nickel sample under various 
static stresses. Suppose the sample is originally at the 
retentivity Bo. A compression and a positive field Ho 
bring the .sample to state A. Since a stress is eciuiva- 
lent to a field, state A is magnetically eciuivalent to 
state .4'. Accoi'ding to the rules, the sample will re¬ 
turn to state Bo after the comjjression and the field are 
remoA’ed, unle.ss the former is so large as to deform 
the sample plastically. On the other hand, a tension 
Po and a field —Ho bring the sample to the state C 
which is eciuivalent to C'. In this case, the sample 


calling for small demagnetization of a transducer 
operated at retentivity limits the magnitude of the 
driving field, the exciting stress, and the mechanical 
Q. When detailed experimental data are available, it 
is possible to set an upper limit to the extent of de¬ 
magnetization and find the optimum values of Q and 
of the maximum exciting stress, on condition that the 
available acoustic output is a maximum. Without de¬ 
tailed data it is more advantageous to choose a small 
Q, since the output of a given transducer is propor¬ 
tional to Q and to the scpiare of the amplitude of the 
exciting stress. 


CONFIDENTIAL 

















































100 


MAGNETIC AND MAliNETOSTKICm E PKOPEKTIES OF MATEKIAI.S 


1.8.3 Some Experimental Tests on 
Half-Hard A-Niekel and 2V-Permendiir 

Consideration can now he devoted to the maximum 
exciting stre.sses that can be set up in half-hard 
A-nickel and 2V-Permendur transducers without too 
much demagnetization, assuming that the mechani¬ 
cal Q's are small. For half-hard A-nickel, Figure .50 
shows that the maximum safe peak field is about 
15.4 oersteds, corresijonding to minor loop 1. Some 
minor loops for 2\"-Permendur have already been 
shown in Figure 17. The minor loop at the top of that 



0 100 200 


TEMPERATUHE-C 

Figure .56. Variation with tcmirerature in resistivity 

of oxide-annealed .\-nickel. 

figure is about as large as can safely be used. Thus a 
maximum peak field of 14 oersteds is obtained. To 
find the corresponding peak-exciting stresses Po, loop 
1 in Figure .50 and the .small loop in Figure 17, to¬ 
gether with the data in Figures 4.3 and 47, are used 
to integrate XdB' along half of each minor loop. 
Theoretically, the clamped-core minor loops shotdd 
be used to calculate the exciting stre.sses. However, 
becau.se of the small values of the electromechanical 
couitling coefficient of the half-hard materials, the 
minor loop of a free sample is only a little different 
from the cori-esi)onding loop of the clamped .samjile. 
Therefore the ap])roximation is justified. Because of 
the presence of terms proportional to the square of 
B', the values oiJ'XdB' for the two halves of each 


minor loop differ to a .small extent. Taking the rms 
values of the integrals as Po, 

Po = 3.94 X 10'* dynes per .sq cm for half-hard 
A-nickel, 

Po = 8.45 X lO"^ dynes per scj cm for half-hard 
2 ^'-Permendur. 

Thus the maximum available power output of a 
transducer made of half-hard 2\'-Permendur is about 
4.5 times as large as that of a similar unit made ot 
half-hard A-nickel. 



Figure .57. Variation in B' with temperature of 
annealed .\-nickel. 

Becau.se it is not known how small the mechanical 
Q should be, some tests of prolonged “driving” in 
water at a peak field of 16.5 oersteds were made on 
half-hard A-nickel (0.00.5-in. laminations, 1 hour at 
600 C) and 2\'-Permendur (0.006-in., 1 hour at 
.500 (’). The samples used were 60-kc ring stacks 
with 1.04-in. mean diameters and 0.165-in. wall 
thickne.s.se.s. The mechanical Q's of these stacks in 
water were of the order of 6. Each sample was first 
magnetized to the retentivity and then subjected to 
continuous reversals of a decreasing d-c field, starting 


CONFIDENTIAL 





























































EFFECT OF TEMPERATURE ON PROPERTIES OF A-NICKEL 


101 


from 16.5 oersteds, so that the remanence was 
brought to the middle of the minor loop that was 
traced out by the first few reversals of a field of 16.5 
oersteds. Impedance measurements were then made 
with both samples in air. Next, each sample was im¬ 
mersed in water in an absorbent-lined tank and 
driven by alternating current at resonance, with the 
current increasing slowly from zero to a value cor¬ 
responding to a peak field of 16.5 oersteds. 



TEMPERATURE-C 


Figure 58. Variation in reversible permeability with 
temperature of A-nickel. 


In the case of the Permendur sample, pronounced 
cavitation was noticed from the noi.se and gas bub¬ 
bles created by the vibrations of the sample at the 
higher fields. In the case of the nickel sample, cavi¬ 
tation was barel}^ noticeable at 16.5 oersteds. In 
general, cavitation did not seem to be a good criterion 
for estimating the output power, because it de¬ 
pended greatly on whether the sample was in the 
tank, which simulated an open field, or in an en¬ 
closed vessel where standing waves cau.sed cavita¬ 
tion to .set in at a much lower power level. 

After about thirty minutes’ driving, the alter¬ 
nating current was slowly decreased to zero and the 
sample was taken out of water, dried, and checked 
by impedance measurements. For the Permendur 
.sample, the motional impedance circle was practi¬ 
cally the .same as that obtained before driving, indi¬ 
cating that the remanence of the core had not 
changed. In the case of the nickel .sample, the diam¬ 
eter of the motional impedance circle decrea.sed by 
about 10 per cent, indicating that the .sample had 
been demagnetized slightly by the driving. Since the 
(.liameter of the motional impedance circle is propor¬ 
tional to and since p does not vary significantly 
for a small variation in B' (see Figure 17), an estima¬ 


tion made with the help of Figure 43 shows that 
remanence had decreased by aliout 100 gausses. 

The relative acoustic output as a function of driv¬ 
ing field was also observed. It was found that up to 
the maximum peak field of 16.5 oersteds the .sound 
pressure was very nearty proportional to the square 
of the peak field and had practically no harmonic 
distortions. This should be the case, since for driving 
fields of such magnitude the minor loops are short, 
straight, and almost parallel to one another and the 
variation of X with B' is also linear. 



0 100 zoo 


TEMPERATURE- C 

Figure 59. Young’s Moduli of A-nickel as affected by 
temperature and impo.sed magnetic field. 

4.9 EFFECT OF TEMPERATURE ON 
PROPERTIES OF A-MCKEE 

In testing elements of various magnetostrictive 
multielement transducers in this laboratory, it was 
frequently noticed that the characteristics of the 
elements varied to a certain extent with fluctua¬ 
tions in room temperature. This phenomenon was 
most conspicuously exhibitefl by variations in the 
re.sonant frequency, which was often measured to 
within 2 to 3 c. Since some of the transducers 
had to meet a number of close specifications for 
satisfactory operation, it became desirable to study 
the phenomenon in more detail under controlled 
conditions. The problem is also of importance for 
two other reasons. First, a transducer used as a 
high-powered projector has numerous internal losses 
which tend to raise the temperature of the transducer 
and change its characteristics. Second, previous in¬ 
vestigations^- have shown that the E effect (change in 
E with magnetization) in nickel becomes large as the 
temperature increases and reaches a maximum at 
about 180 C, indicating that the electromechanical 
coefficient may be much higher at elevated tempera¬ 
tures than at room temperatures. For this reason, 
some detailed measurements were carried out on 
A-nickel. 


CONFIDENTIAL 


































102 


MAGNETIC AND MAGNETOSTRlCTI\ E PROPERTIES OF .MATERIALS 


The sample used for these measurements was No. 1 
of the 0.010-inch oxide-annealed samples of which 
the magnetization curves at room temperature are 
shown in Figure 7. It contained 26 laminations of the 
same mean diameter and wall thickness as those 
listed in Table 2. The laminations were loosely tied 
up at three points by thin glass-fiber cords to form a 
composite ring, with oxide films the only insulating 
material between the laminations. 



Figure 60. Magnetostrictive coefficient and co¬ 
efficient of electromechanical coupling of A-nickel a-s 
affected by temperature. 


The sample was installed in a somewhat different 
manner from that described earlier in this chapter. 
A toroidal brass cup, which had a cross section about 
3^ X 3^2 thickness 3^2 di., replaced the 

wood frame. The nickel ring stack was freely sus¬ 
pended inside the toroidal cup by No. 35 copper wire, 
which formed three loops supported by horizontal 
glass rods held across the top of the toroidal cup bj^ a 
high-temperature cement. 

The outside of the cup was then coated with a 
layer of Insalute cement. When this coating was dry, 
two coils (10 and 120 turns respectively) of No. 35 
bare copper wire were wound on the toroidal cup. 
These served as search coils for measuring B' and n' 
and were also coated with Insalute so that both were 
well insulated and protected turn by turn. The leads 
of these coils came out through alundum tubes. 


A primary coil consisting of 136 turns of No. 14 
bare copper wire was wound uniformly on the toroid 
to serve as magnetizing coil in the magnetic measure¬ 
ments and as a-c dri\dng coil in the dynamic measure¬ 
ments. This coil was also jmrtly coated by Insalute 
to insure good insulation. The whole assembly was 
then baked at 300 F for a day to dry and harden 
the Insalute cement. 

Before the measurements were carried out various 
tests were made to be .sure that the coils were insu¬ 
lated from one another and that each was insulated 
from the brass cup. The whole assembly was then 
placed in an oven which was capable of maintaining 
a maximum temperature of about 250 C. The leads 
of the three coils were protected by alundum tubes 
and were led out of the oven through small openings. 

The temperature was measured both by a mercury 
thermometer and a copper-constantan thermocouple 
whose hot junction was located close to the nickel 
ring stack. In general, the temperature was accurate 
to about 1C. In the magnetic measurements, how¬ 
ever, the temperature sometimes fluctuated by as 
much as 4 C because of the heating effect of the 
magnetizing currents. 

Resistivity measurements were made on a single 
ring lamination in the manner already described. 

The normal magnetization curves and the ti' vs H 
curves are shown on different scales in Figures 52 to 
55. From these curves it can be seen that at a given 
field both the intensity of magnetization and the re¬ 
versible permeability vary with temperature. The 
.sense and magnitude of the variations are, however, 
greatly dependent upon the strength of the field. 
This is due to the fact that different quantities which 
vary with temperature are in predominant control 
of the intensity of magnetization and the reversible 
permeability in different ranges of the field. 

In addition to the intensity of magnetization and 
the reversible permeability, the coercive force was 
also observed. It was found to decrease steadily from 
1.4 oensteds at 22 C to 0.79 at 221 C, indicating that 
the hysteresis decreased steadily with increasing 
temperature. This decrease in hysteresis accounted 
partly for the increase in the reversible permeability. 

The variation of the resistivity with temperature 
is shown in Figure 56. It is seen that its value at 
200 C is just double that at 20 C. 

Impedance measurements were made at ^■arious 
temperatures for two polarizing fields, 22.0 and 37.4 
oersteds. At 22 C, a field of 22 oersteds is close to that 
at which the electromechanical coupling coefficient 


CONFIDENTIAL 











































EFFECT OF TEMPER ATI IRE ON PROPERTIES OF A-NICKEL 


103 


is a maximiun. Figures 57 and 58 show the induetion pe of Figure 55, the effective thickness of laminations 
B' and the reversible permeability p' as functions of that fits the experimental values of f is 0.012 in. as 
temperature at these two values of the field. These against the actual value of 0.010 in. 

Table 9. A summary of impedance and magnetic measurements for oxide-annealed 10-mil 
A-nickel, with Ho equal to 22.0 oersteds. 


Temp, C 

4ir/o 

gausses 

m' 

f 

degrees 

Rc 

ohms 

ohms 

h 

fr 

kc/sec 

Da 

ohms 

Qa 

Pot eff 
per cent 

22 

3795 

67.8 

31.7 

18.6 

27.3 

58.4 

19.91 

51.1 

18.1 

56 

48 

3830 

77.0 

29.9 

17.4 

29.0 

60.1 

19.73 

67.5 

15.5 

82.9 

67 

3850 

81.3 

30.0 

18.6 

32.3 

66.5 

19.58 

73.1 

14.0 

87.6 

107 

3835 

84.0 

28.5 

19.5 

36.0 

71.9 

19.38 

84.2 

13.8 

87.9 

149 

3770 

80.8 

26.0 

19.0 

40.1 

75.9 

19.33 

98.2 

15.9 

92.0 

190 

3690 

75.6 

22.8 

17.6 

41.6 

73.8 

19.38 

113.4 

22.0 

86.9 

224 

3615 

69.6 

20.1 

16.1 

40.2 

68.0 

19.47 

122.2 

32.5 

79.1 


Table 10. A summary of impedance and magnetic measurements for oxide-annealed 10-mil 
A-nickcl, with Ho equal to 37.4 oersteds. 


Temp, C 

47r/o 

gausses 

m' 

degrees 

Rr 

ohms 

Ay 

ohms 

M 

fr 

kc/sec 

Da 

Qa 

Pot eff 
per cent 

22 

4760 

30.7 

16.4 

5.8 

19.7 

31.0 

19.84 

62.3 

31.0 

79 

49 

4800 

32.9 

18.5 

6.8 

20.5 

33.3 

19.79 

64.7 

26.4 

88 

73 

4820 

34.2 

17.8 

6.5 

21.0 

33.9 

19.67 

68.7 

27.0 

94 

112 

4800 

34.6 

16.8 

6.7 

22.3 

35.7 

19.60 

75.7 

30.6 

87 

151 

4660 

32.3 

15.5 

5.9 

22.4 

35.2 

19.67 

81.2 

37.8 

93 

193 

4440 

26.4 

11.8 

4.1 

19.1 

28.8 

19.80 

88.0 

79.2 

87 

235 

4300 

18.4 

7.5 

2.3 

13.5 

19.5 

19.98 

86.6 

175 

82 


last figures are derived from the curves in Figures 
52 to 55. 

The data obtained from impedance measurements, 
together with those obtained from magnetic measure¬ 
ments, are summarized in Tables 9 and 10. In these 
tables, 47r/o and p' are interpolated from the curves of 
Figures 57 and 58. All the other quantities in these 
tables, except p and the potential efficiency, are ex¬ 
perimentally determined and have appeared in pre¬ 
ceding tables, so that no further explanation is 
needed. The ^'ahles of the clamped-core reversible 
permeability p are calculated from Xc, fc, and fr. A 
comparison of the \’ahies of p with the corresponding 
\ ahies of p' and a calculation of the values of the 
electromechanical coupling coefficient show that sev¬ 
eral values of p in Table 8 are somewhat too small, 
while those in Table 9 are in general too large. How- 
evei-, these discrepancies are believed to be due largely 
to errors in the polarizing fields rather than to errors 
in f and the interpolated values of A^. 

As in the case of several of the samples discussed 
in Section 8, the calculated values of p do not check 
with the eddy-current theory without discrepancy. 
Taking the calculated values of p and the values of 


The values of the potential efficiency in the last 
columns of Tables 9 and 10 are calculated from Rc, 
j', and Da- Owing to large errors in the interpolated 
values of Rr, these are only aj^proximate. However, 
the potential efficiency shows a general tendency to 
increase with increasing temperature, reaching a 
maximum at about 150 C, and then to decrease again. 

The Young’s moduli E' and E, the electromechan¬ 
ical couijling coefficient k, and the magnetostrictive 
coefficient X are plotted as functions of temperature 
in Figures 59 and 60. 

All the data are now available from which a con¬ 
clusion may be reached as to what takes j^lace in a 
nickel magnetostrictive transducer when it is heated 
up. It will be assumed that the transducer is polarized 
at room temperatures by a constant field to an in¬ 
tensity corresponding to the maximum of k. From 
previous calculation it is known that both p and X 
increase as the temperature is raised. Ck)nsequently, 
the electromechanical coupling coefficient increases, 
but its increase is largely due to the increase of p. 
The rapid increa.se of the electric resistivity more 
than compensates for the increase of p, so that the po¬ 
tential efficiency increases rather than decreases. But 


CONFIDENTIAL 



































101 


MAGNETIC AND MAGNETOSTKICTIVE PROPERTIES OF MATERIALS 


the potential efficiency does not tell the whole story, 
since it applies only to low power levels. We know 
from the magnetic measurements that the rajiid in- 






.010" A NICKEL 
OXIDE ANNEALED 


/ 

/ 

/ 










/ 

/ 

/ 










4 












/ 








2 2 

/u 


/ 








/ 

/ 

/ 



L- 







/ 

/ 

'224 


/ 

H = 

37.4 







/ 

/ 

/ 

H = 2 

2.0 








/ 

/ 

/ 










/ 

/ 

/ 










/ 

/ 


5 MIL OXIDE ANNEALED 
A NICKEL AT 22‘’C 




/ 

/ 










/ 

/ 

/ 










/ 

/ 

✓ 












0 1000 2000 3000 4000 5000 

B' 


Figure 61. Variation of magnetostrictive constant of 
A-nickel with B' and temperature. 

crease in resistivity is also accompanied by a decrease 
of hysteresis. Therefore, for a transducer operating 
at high power levels, an increase in temperature 
will probablj' reduce the lo.sses appreciablj'. 


As a result of the increa.se in electromechanical 
coupling, Young’s modulus E', and therefore the reso¬ 
nant frequency, decreases since E does not vary 
noticeably until the temperature is well beyond 
100 C. In general, the effect of thermal expansion 
also tends to decrease the resonant frequency, but the 
effect is small. For nickel, the coefficient of thermal 
expansion between 0 and 200 C is about 14 X 10“b 
Thus, for our ring stack at 200 C, thermal expansion 
alone reduces the I’esonant frequency by about 0.3 
per cent. The values of E' in Tables 9 and 10 have 
been corrected for this effect. Taking both of these 
effects into account, results show that for a 10-mil 
oxide-annealed A-nickel tran.sducer polarized to 
about the optimum intensity at room temperature 
the resonant freciuency decreases by about 0.035 per 
cent per degree centigrade between 20 C and .50 C. 

The variation of X with temperature is not entirely 
clear theoretically. In any ca.se, results show that it 
increases slightly between 20 and 50 C. Beyond 50 C 
it begins to decrea.se steadily. The values of X are also 
plotted against A-kI in Figure 61, in which the curve 
for 5-mil oxide-annealed A-nickel is reproduced for 
comparison. It should be noted that the values of X 
are calculated from k-, E, and /i, .so that errors in the 
values of /j are also introduced into the values of X. 

At the two \ alues of the polarizing field used, n 
reaches a maximum at about 150 C. Beyond 150 C, 
the simultaneous decrease of X and ^ causes the 
electromechanical coupling to drop .sharply. For this 
rea.son the jjotential efficiency begins to decrease even 
though n decreases and pe continues to increase. 


CONFIDENTIAL 







































Chapter 5 


DIRECTIVITY PATTERNS 


5.1 INTRODUCTION 

The pre.ssure field of a sound source depends on tlie 
condition of the medium through which the sound is 
propagated, the disposition and surface condition of 
the baffles, and the shape, size, and physical char¬ 
acteristics of the source itself. The medium, usually 
water, is assumed to be uniform, that is, of constant 
density and velocity of sound transmission. The 
baffle conditions will always be stated; in most of the 
cases treated here, there is either no baffle or an 
infinite-plane baffle. Under certain conditions, such 
as when the dimensions of the source are large com¬ 
pared with the wave length of the signal, the pattern 
may be independent of the source baffle conditions. 

5.1.1 The Problem 

Here the main concern is with the dependence of 
the pressure field on the shape and size of the source 
and with the effect of \’arying the amplitude and 
phase of different portions of the active surface of 
the radiator. 

5.1.2 Definition of Pattern 

Throughout this discussion, the distance between 
the source of sound and the point of reception will be 
assumed to be large compared with the dimensions of 
the source. This allows considerable simplification 
in the analysis and is the usual practice. The distribu¬ 
tion ill angle of pressure amplitude at a large fixed 
distance from the source is called the pressure ampli¬ 
tude pattern or directivity pattern of the source. 
There is some occasion for referring to the distribu¬ 
tion of the phase of the pres.sure at a large fixed di.s- 
tance from the source; this is called the pressure 
phase pattern of the source. Since primaiy interest 
here centers in the relative amplitude of the pres¬ 
sure, it is convenient to disregard factors depending 
on distance and to normalize the amplitude pattern 
to unity in some direction, usually the direction of 
maximum sound amplitude. 


5.2 RECIPROCITY THEOREM 

An acoustic reciprocity theorem applies to all the 
calculations shown in this chapter, that is, the direc¬ 
tional jiattern in transmission is the same as that in 
reception, provided the term directional pattern is 
understood in the proper sen.se. The reciprocity 
theorem in its most general form may be stated as 
follows: 

Let an enclo.sed region have bounding suifaces 
5i, 82 ,- ■ ■, and let the two distributions, generally 
different, of normal velocities v' and v" over the 
bounding surfaces produce pressure fields p' and p" 
respectively in the enclosed region. Then 

f (pV - pV)d 8 = 0. 

Jsi. St. ■ ■ ■ 

To obtain the reciprocity theorem in the simple 
form u.sually used, take as two of the bounding sur¬ 
faces a microphone or transmitter with associated 
baffles and a spherical source with radius a that is 
small compared with the wave length of the signal. 
Furthermore, let v' be zero except at the microphone, 
and let v" be zero except at the spherical source, 
where it is the radial velocity of the surface. The 
quantity 47 ra'V' is called the strength of the spherical 
source and is denoted by Q,. Then the ecpiation 
above becomes 

f phv'dM = Q,p,', 

Jm 

where p^ is the pressure on the microphone M when 
the simple source is used as a transmitter, and p/ is 
the pressure on the simple source when the micro¬ 
phone is used as a tramsmitter. This equation states 
that the pressure at any point 8 caused by a given 
velocity distribution on a microphone is the same as 
the total pressure on the microphone (diaphragm 
held rigid) caused by a source of unit strength at 8 , 
the elements of area of the microphone being 
weighted in accordance with the original velocity 
distribution. 


CONFIDENTIAL 


105 


106 


DIRECTIVITY PATTERNS 


5.2.1 Constant Velocity Source 

If a microphone with constant velocity over the 
diaphragm is used as transmitter, 



Thus reciprocity holds if (1) the directionality in 
transmission is taken as the pressure at distant points 
in various directions caused by unit velocity of vibra¬ 
tion of the ti’ansducer-microphone, and (2) the direc¬ 
tionality in reception is taken as the total force on 
the rigid diaphragm caused by sound incident on the 
microphone from distant sources of unit strength in 
various directions. 

In applying the theorem of reciprocity, care must 
be taken to use it only for conjugate quantities, for 
example, the normal velocity in transmission and the 
weighted total force on a rigid diaphragm in re¬ 
ception. 

There is no simple relation between the motion of 
the diaphragm in transmission and in reception. If 
the mechanical impedance of the diaphragm is not 
large compared with the acoustic impedance of the 
medium, there is no longer justification for applying 
the reciprocity theorem directly to velocity and 
pressure, as was done above, because the diaphragm 
is then not rigid. Instead, it must be applied to the 
whole electromechano-acoustic system, including the 
electric circuits and mechanical connections of the 
microphone. 

Ballantine “ has extended the reciprocity theorem 
to general electromechano-acoustic systems. As a 
further illustration, consider the application of his 
theorem to a microphone. If a voltage E' applied to 
the microphone produces a pressure Pj in the sound 
field and a source of strength Q'^ at the same point 
produces a current 7" when the microphone output is 
short-circuited, then Ballantine’s theorem gives the 
result that 

Again, only open-circuit voltage and .short-circuit 
current are conjugate in the sense of the reciprocit}' 
theorem. The voltages in transmission and in re¬ 
ception cannot be related without a more detailed 
knowledge of the terminating impedances of the cir¬ 
cuits involved. 

Ballantine’s theorem applies to any linear passive 
.system, even when it includes damping forces, pro¬ 
vided the}' are linear. 


5.3 POINT SOURCES 

A small sphere whose radius expands and contracts 
sinusoidally has a pattern uniform in all directions. 
The source described is commonly called a simple 
point source. If the radius is not small compared 
with the wave length of the signal, the pattern is 
still uniform in direction. Uniformity of pattern holds 
appro.ximately for a radiator of any shape, pimuded 
its dimen.sions are small compared with the wave 
length of the signal, and provided its various por¬ 
tions are not too badly out of phase with one another. 
This is illustrated by considering the pattern of two 
point sources. If the point sources are equal in 
strength and have a phase difference of 2\l/, the pat¬ 
tern is given by 

/ttg . \ 

P = cos I — .sm 7 -f >7 ) ’ 

where a is the distance between sources, X is the wave 
length of the signal, and y is the angle between the 
direction of ob.servation and the normal to the line 
joining the sources (see Figure 1). The patterns 
when ^ = 0 and a = \ 4, X/2, X, and 2X are shown 
in Figure 2. It is clear that if 2\p ^ 180°, then as a 
becomes smaller the pattern becomes independent of 



Figure 1. Relation between point .sources and direc¬ 
tion of observation. 


7 and therefore uniform. For example, if the point 
sources are in pha.se (\p = 0), and if a = X /20, then 
the pressures in the two directions 7 = 0 and y = 90° 
differ by only 1 per cent. If the same two point 
sources are out of phase by 90 degrees (24/ = 90°), 
then the pressures in the two directions differ by 18 
per cent. This illustrates that uniformity of pattern 
depends upon the relative pha.ses of the parts of the 
source. 

5.3.1 Dipole Sources 

In fact, if 24 / = 180°, so that the point sources are 
of opposite phase, for small a, 

Tra . 

U = — sm 7 ) 

X 


CONFIDENTIAL 







POINT SOURCES 


107 




d = x. 



0-2X 


Figure 2. The pattern of two point sources separated by distance a for various values of a. X is the wave length of the 
signal. 


which is not uniform in angle no matter how small a 
is. This source, consisting of two near-by point 
sources which are 180 degrees out of phase, is called 
a dipole source. The normalized pattern of a dipole 
source in a plane through the dipole is shown in 
Figure 3. It has the property of having zero j^ressure 
in the plane normal to the line of the dipole. The di¬ 
rectivity ratio of a dipole is as compared with 1 
for a simple point source. 

5.3.2 Pattern of Array of Point 
Sources 

To obtain the pattern of an array of N simple point 
sources in a baffleless space, let the positions of the 
point sources be determined by the radius vectors 
ri, T 2 , ■ • - , r.v drawn from an arbitrary origin 0. Then 
the directivity pattern of this array of .sources is 

P = (1) 

n = l 

where Q„ and lAn are the strength and pha.se respec¬ 
tively of the nth source, u is the unitv ector in the 
direction of observation, and Pq is a normalizing 
factor which will usually be cho.sen to make P unity 
in the direction in which it is a maximum. The cjuan- 



Figure 3. Pattern of a dipole source. 


CONFIDENTIAL 

























































108 


DIRECTIVITY PATTERNS 


tity k is one that occurs ciuite often in the theory of 
patterns; it is called the wave number of the signal 
and is given by 



where X is the wave length of the signal. The usual 
vector dot product notation is used in writing u • r„. 



[-— a--a-- a —H 

Figure 4. Relation between point source.s and direc¬ 
tion of ob.servation. 

Pattern Parameters 

It is evident from equation (1) that there are 
three independent variables (parameters) which de¬ 
termine the pattern of an arra}' of point sources: 




(1) the configuration of the array itself as determined 
by the relative distance between point sources, etc., 

(2) the relative strengths of the point sources, and 

(3) the relative phases of the point sources. 

Shading 

To show how each of these variables affects the re¬ 
sulting pattern, con.sider four point sources on a 
line. Suppose first that they have the same pha.se and 
are equally spaced a distance a apart, but that the 
middle two point sources are stronger than the outer 
two in the ratio of ic to 1. The resulting normalized 
pattern is given by 



where y is the angle between the direction of obser\'a- 
tion and the normal to the line of the sources (see 
Figure 4). A family of patterns is shown in Figure 5 
for a = X/2, or ka = tt, and iv = 1, 2, and 4. 

Notice that as w is increased, the minor lobes decrease 
and the major lobe becomes bi-oader. 




Figure 5. The jiattern of four sources, equally .spaced one-half wave length apart and having the same phase. W i.s the 
ratio of the strengths of the middle two sources to the two outer source.s (see Figure 4). The solid curve is for point 
sources, the dotted curve for line sources one-half wave length long. 


CONFIDENTIAL 







































POINT SOURCES 


109 


Spacing and Phasing 

Next suppose that the four point sources have 
eciual strengths and phases but that the distances 
lietween successive points are ai, a^, and ai (see 
Figure 6). Then the pattern is 


P = 


1 

2 


cos 




A'(cto T 2(ii) 

2 


sin 



In Figure 7, patterns are drawn in which + 2ai is 
held constant at 3X 2, and the quantity 


02 

CI 2 T 2fli 




Figure 6. Relation between point sources and direc¬ 
tion of observation. 


has the values 1, y^, Yi, and 0. Again it will be noticed 
that as the strength density increases at the center 
of the line of sources the major lobe becomes broader 
and the minor lobes become smaller. 



Figure 8. Relation between point sources and direc¬ 
tion of observation. 


Finally, suppose the point sources have equal 
strength and are equally separated by a distance o, 
but the phases are not the same (see Figure 8). If 
’An 'p 2 , 'Ph and xpi are the phases of the successive 
j)oint sources, the pattern is given by 

(3ka . \ (ka . N 


F = Po 


+ e 

+ e - + e “ 



w = I 





Figure 7. The pattern of four point sources of equal strength and phase, symmetrically spaced on a line. IF is the ratio 
of the distance between the inner point sources to the distance betw'een the outer point sources, the latter being assumed 
fixed at one and one-half w'ave lengths (see Figure 6). 


CONFIDENTIAL 










































no 


DIR ECTIMT V P A FTER NS 


Consider the case in which there is progressive 
phasing, so that i/'i = = 'A, ^3 = — andi /'4 = 

— 3i/'. Then the pattern is 


P = 


2Po 


cos 


/Ska . 
smT 



+ cos 


(ka 

sin 7 



The amplitude pattern of P is shown in Figure 9 
when a = X/2 and 4' = 30°, 45°, 60°, and 75°. It will 
be noticed that the pattern is somewhat the same as 
one in Figure 5, except that the major lobe is shifted 
by an amount approximately ? 3 ’A- 


where <f> = ka sin 7 , and 7 is the angle between the 
direction of observation and the normal to the line 
of the sources. Po is given by 


K 


n 


and the directivity ratio (.see Section 5.7) of the 
jiattern is 


D = Pi ZT. 


sin ka(m + n) 
ka{m + n) 





Y = 60“ 


VJ/ = 75” 


Figure 9. The pattern of four point sources of equal strength equally spaced one-half wave length apart and progres¬ 
sively phased by an amount 2\j/ (see Figure 8). 


5.3.3 Equally Spaced Point Sources 
on a Line 

Suppose that N point sources are equally spaced a 
distance a apart on a line and that all the sources 
have the same phase. The pattern is then given bj^ 

P = PoZQne^"\ (3) 

n 


Fourier Rel.vtion between Source Strengths 
AND Pattern 

It is clear that equation (3) gives the expansion 
of the pattern P in a finite Fourier series. Thus the 
coefficients which are the strengths of the point 
sources, are related to the pattern by the formula 



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POINT SOURCES 


111 


If the source is symmetrical (Q„ = Q_„), it is more 
convenient to use the cosine form 


P = 


Pu 


{N-1)/2 

Qo + 2 XI Qn cos tl<l> 

71=1 


(5) 


for the case where the center of symmetry falls at 
one of the point sources, and 


P 


2Po 


1 cos (n - \)<i> 


= 1 n—3 


( 6 ) 


for the case where the center of symmetry falls mid¬ 
way between two of the point sources. In the former 
case N is odd, in the latter case N is even. In either P 
is symmetrical and 


The importance of the Fourier relationships be¬ 
tween P and Qn is that they permit “designing” for 
a given pattern P without recourse to a long trial- 
and-error procedure which may or may not be suc¬ 
cessful. That is, for any given pattern P, equation 
(4) gives the required strengths of the point 
.sources directly. Of course, for an arbitrary P, Q„ will 
not be zero for large n, so that in general an infinite 
number of point sources are required to fit a given 
pattern. This requires that a compromise be made 
in choosing the pattern P to be approximated or in 
choofsing N large enough so that the contribution of 
the neglected point sources is below some prescribed 
amount. 


Designing for Gaussian Pattern 

To illustrate the above, find the line of equally 
spaced points which will produce the radiation pat¬ 
tern 

P = (8) 

where <j) = ka sin y and A is a parameter determining 
the width of the pattern. From equation (7), 

^ 2 r -(^/A)2 

= - I e cos n<t>a(l> • 


If e is small compared with unity, the integra¬ 

tion may be extended to infinity, with the result that 


Qn 


_ jX ^-(n^AV4) 
"Vtt" 



(9) 


where the notation in Jahnke and Emde has been 
used for the second derivative of the error integral. 
In this equation n is either an integer or half an odd 
integer, according as the center of symmetry coin¬ 
cides with one of the point sources or is midway be¬ 
tween two of them. Since Q„ is not zero for finite n, 
the Gaussian pattern (8) requires an infinite num¬ 
ber of point sources for its exact representation. 
However, only a reasonable approximation of this 
pattern is required, therefore terms beyond a certain 
point in the series are omitted. This introduces 
minor lobes into the pattern. Minor lobes can be 
made sufficiently small if care is taken not to omit 
terms in (.3) which contribute a significant amount. 
Because the coefficients in (9) fall off so rapidly with 
increasing n, the first omitted term is by far the 
most important and the height of the minor lobes 
can be .said to be about twice the first omitted co¬ 
efficient. 

This procedure will be illustrated by a numerical 
example. Suppose that a radiator is desired with six 
point .sources and with total width of two and one- 
half wave lengths, that is, the distance between 
adjacent point sources is X/2. The minor lobes must 
be no higher than —30 db compared with the 
central lobe. The width of the major lobe cannot be 
specified, as enough quantities have already been 
fixed to determine it. Since there are an even number 
of point sources (six), the pattern is given by 



where Qn is given by equation (7). Only three 
terms of the series have been used, each term cor¬ 
responding to two point sources of the radiator. 
The coefficient O 1/2 is the amplitude of the central 
two point sources, Q 3/2 of the next pair, and Q 5/2 of 
the outside pair. The first omitted coefficient is O7/2 
and this must be small enough so that its omission 
will not reintroduce minor lobes higher than —30 db 
(3.16 per cent). It is desirable to make 2 Q 7/2 no 
smaller than 0.0316, because a smaller value would 
reduce the minor lobes unnecessarily below —30 db 
and, at the same time, broaden the central lobe, that 
is, require a larger A. Also the maximum power which 
could be radiated would be smaller because of the 


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112 


DIRECTIVITY PATTERNS 


smaller amplitude on the outside point sources. 
Since 



A must be found so that 

"" -^(0 0316) = -0.1106. 

From Jahnke and Emde,“^ 7il/-l is found to be 1.687, 
so that A is 0.964. Further calculations show that 

Qi/2 ~ 0.514, Q 3/2 ~ 0.322, Q,5/2 — 0.128 

and 

,777 = Qi/2 + Q3/2 + Q5/2 = 0.964 • 

Jir 0 

The pattern (see Figure 10 ) is then 
P = 0.533 cos sin 7 ^ + 0.334 cos sin 7 ^ 

+ 0.133 cos sin 7 ^ • 

It is 32 degrees wide, 6 db from the peak, and satis¬ 
fies the imposed minor-lobe requirement. 




Figure 10. The pattein of .six point sources spaced 
one-half wave lengtli apart and shaded to have minor 
lobes lower than 30 dh below the peak of the major 
lolie. 

In the pattern just discussed, the distance between 
adjacent point sources was arbitrarily taken to be 
X/2. In the design of a radiator of point sources, spac¬ 
ing must be selected for the point sources. Theoreti- 
call,v the maximum spacing is one ivave length, but in 
practice it nnisthe considerably less. Consider the Fou¬ 
rier series (5) and ( 6 ); the first has a period 2-71 in 
(j), whereas the second has a period of drr in 4 >, but at 
the point -j- 27r it has the negative of the value at 


<t> (.see Figure 11). Thus, in both cases, the intensity 
pattern w'hich is proportional to the square of the 
pres.sure has a period of 27r. In the physical problem 
only a finite rather than an infinite range of </> must 
now be considered. In fact, since 4) = (27rfl/A) .sin 7, 
<p ranges between the limits ± 2wa/X as 7 is varied 
between its limits of ± tt 2. If 2x0/ X > 2x, that is, 
if a > X, it is clear that the jjhysical range of (p in¬ 
cludes not only the central major lobe at </> = 0 but 
also the two major lobes at 4> = + 2x. Since this is 
a situation which should be avoided, the relation 
o < X must be maintained. Actually, the spacing a 
should be enough smaller than X so that the physical 
range of 0 does not go beyond the point .4 which 
marks the beginning of the second lobe in Figure 11. 


Figure 11. Illu-stratine; pattern for equally spaced 
point sources on a line, .\ for the odd number of sources, 

B for the even number of sources. 

The above analysis can be applied with minor 
modifications to a line of etpially spaced point sources 
with a progressive shift in phase of an amount \p be¬ 
tween points. There is the same pattern of eiiuations 
(3), (5), or ( 6 ) but with 

2 ira . 

0 = sin 7 — 0 • 

The preceding discussion makes use of the fact 
that with 0 = 0 the physical range of 0 is between 
+ 2xa X. With phase shift 0, the limits are +2xa X 
— 0. The largest value of 0 to be used is 0 = 2xa/X, 
corresponding to a shift of 90 degrees in 7. For this 
shift the limits on 0 are 0 to — 4xa/X which, as in the 
]n-eceding section, must be within +2x. Hence when 
a large progressive phase shift is to be used, a < X/2 
must be true. 

Ajiply equation ( 1 ) to obtain the pattern of N 
point sources equally spaced on a line, assuming that 
all the point sources have the same strength and 
phase. Let the origin 0 be on the line of the sources 




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LINE SOURCES 


113 


a distance Oq from the first source, and let the dis¬ 
tance between successive sources be a. Then 


^0 XI 


jA-[rii)+(n —l)a] siny 


where y is the angle between the direction of observa¬ 
tion and the normal to the line of the sources. This 
expression can be summed up to give 


P = 



^klao+a(.\ — l) /2]sin y 


Thus, if Oo = — {N — l)a/ 2 , which places 0 midway 


indefinitely while keeping (iV — l)a = Z constant. 
Thus the pattern of a uniform line source of length 
I is 



kl . 

-SUIT 


( 11 ) 


This pattern is .shown in Figure 13 plotted against 
the universal parameter (Z/X) sin y. This pattern is 
important since, as will be seen later, it is also the 
pattern of a square in a normal plane parallel to the 
side of the square. The highest minor lobe is 13.5 db 



N =6 N = 8 


Figure 12. The pattern of N point sources of equal strength and phase equally spaced one-half wave length apart 
on a line. 


between the two end-point sources, and Po = 1/1 
which normalizes the pattern. 


sm 


P = 


ka . 

N — sm y 


ka . 

N sm I — sm y 


In Figure 12, this pattern is shown with a = X/2 
and N = 3, 4, 6 , and 8 . 


5.4 LINE SOURCES 

The pattern of a line source can be obtained from 
equation (10) by letting N increase and a decrease 


below the major lobe, and the width 27 of the major 
lobe 6 db down is determined approximate!}" by 


sin 7 = 


3X 

51 


so that, if X/Z <3C 1, 


27 = 68.8 ^ degrees. 

For example, if Z = 5X, the major lobe is approxi¬ 
mately 13.8 degrees. 


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114 


DIRECTIVITY PATTERNS 


5.4.1 Directivity Ratio of Line 
Source 

The directivity ratio of a line source is shown in 
Figure 14 plotted against l/X. When l/X » 1, it is 
given by 



In Figure 15 the directivity ratio of a line source is 
shown as a function of the width of the pattern 3, G, 
and 10 db from the peak. These curves are useful 
when the pattern is available and the exact effective 
dimensions of the line source are not known. 

A general formula for the pattern of a line source 
can easily be obtained from equation (1). Thus by 
letting 

Qn = f{j^n)dx 

so that/(j„) is the strength per unit length of the line 
.source at x = x„ (the origin of x is taken at the 
midpoint of the line source), and then by pei'initting 
N to increase indefinite!}' 

ri.2 

P = Po ( 12 ) 

J-1/2 

is obtained where I is the length of the line source; y 
is the angle between the direction of observation and 
the normal to the line source; and the normalizing 
factor, when i/' = 0, is determined by 

1 

p = f(^)dx- 

Ecjuation (11) can be easily verified for the pattern 
of a uniform line source by taking Po = 1 7,/(.r) = 1, 
V' = 0, and integrating. 



1 = SINT 


FuiURE 1.3. The patteiii of ;i line source of lengtli I in 
terms of the dimensionle.ss parameter (//X) sin 7 , where 
X is the wave length of the signal and y is the angle be¬ 
tween the normal to the line source atul the direction 
of observation. 



A 


Figure 14. Directivity ratio D of a line source of length I to a signal of wave length X. When /X )$> 1, then D = \/2l. 


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20 LOG |p| 



























































































LINE SOURCES 


115 


5.4.2 Shading 

Discrete Shading 

The effect of shading on the pattern of line source.s 
when i/' = 0 will be illustrated by considering two 
cases. First suppose that a line source of length I is 
divided into four equal segments, and suppose /(.c) 
= 1 on the outer two segments and /(x) = w, a 
constant, on the inner two segments. The pattern of 
such a .shaded line source is 

sin 4 > 

sin 4 ) {iv —1)2 
4> 2 ^ ’ 

2 


so that the shading is parabolic; w is the ratio of the 
strength at the midpoint to that at the ends of the 
line .source. The pattern is given by 

P = io(<^) + 2^ ’ 

\w + 1/ 

where 4 > = (kl/2) sin y and is the nth spherical 

Bessel function.®’ These patterns for w = 1, 2, 4, • • •, 
oo are shown in Figure 18 and the corresponding di¬ 
rectivity ratio curves are shown in Figure 19. Again 
it is clear that as the shading is increased the major 
lobe broadens while the minor lobes decrease and the 
directivity decreases, that is, the directivity ratio 
increases. 


P = 


2 


ic + 1 



Figure 1.5. Directivity ratio D and directivity index d of a line source .as a function of width 5 of a pattern .3, fi, and 10 db 
fi'om peak. 


where = {kl/2) sin y, and y is the angle between the 
direction of observation and the normal to the line 
source. A family of patterns is .shown in Figure 16 
for w = 1, 2, .3, and 4. As iv increases, the major lobe 
widens, while some minor lobes decrease as others 
increa.se. When w = the minor-lobe energy is 
almost equally distributed among the first three 
minor lobes. Figure 12 shows the patterns when 
I = 2X. The directi\'ity ratios of the patterns in 
Figure 16 are .shown in Figure 17. 

Continuous Shading 

Next suppose the line source of length I is continu¬ 
ously shaded and that 


5.4.3 Prodvict Theorem for Line 
Sourees 

Suppose a line .source of length L is divided into N 
ecpial segments of length I and that f{x) and \l/ are 
constant on each segment, say/(a-) = Q„ and \(/ = ip„ 
on the nth .segment. By applying equation (12) to 
obtain the resultant pattern, it is found that 



where P'o differs from Po by a simple constant factor. 
In the summation, n is integral if N is odd and is half 
an odd integer if N is even. It has just been shown 


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116 


DIRECTIVITY PATTERNS 



Figure 16. The pattern of a shaded segmented line source of length / in terms of the dimen.sionless parameter (f/X) sin y. 
X is the wave length of the signal and 7 is the angle between the normal to the line source and the direction of observa¬ 
tion. TF is the ratio of the amplitude of the two middle elements to that of the two end elements. 


that the pattern of a segmented line source is the product 
of the pattern of a single segment with the pattern of 
point sources having the strengths and phases of the 
segments and situated at similar points of correspoml- 
ing segments. Thi,s is a special case of the more gen¬ 
eral product theorem discu.s.sed later in the chapter. 


For example, the pattern of a line source consisting 
of four equal segments each of length a, all of the 
same phase but with the center two segments being 
w times as strong as the end two, is simply the jtat- 
tern of equation (2) midtiplied by the pattern of a 
line source of length a, or 


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LINE SOURCES 


IIT 



This pattern is shown in Figure 5 for a = X/2 and 
w = 1/^, 1, 2, and 4 (the same cases as for the point 
sources). The improvement of the segmented line 
source pattern over the corresponding point source 
pattern is apparent. 


responds to the Fourier series relation between the 
pattern of a line of point sources and the strengths 
of the point .sources. It follows that 

This permits prescribing the pattern P{4>) and finding 
the shading (/(u) of the line source to obtain the 
pattern. In general gr(u) will not be 0 for [ u | > kl/2, 
no matter how large kl, so that the effect on the pat¬ 
tern of having a line source of finite length must be 
evaluated; that is, the contribution of the neglected 
part of the line .source must be below prescribed 
limits. This is similar to the procedui’e followed for a 



Figure 17. The directivit_y ratio of a shaded, segmented line source of length I to a signal of wave length X. IF is the 
ratio of amplitude of the two middle elements to that of the two outer elements. 


5 . 4 . t Fourier Integral Relation 

between Pattern and 
Strength Function 


If xp is considered to be zero in equation (12) and 
a simple change of variable is made inside the integral 
.sign. 


P{4>) 


rkl/2 

= Po g 

J-kl/2 


g(u)c-'“'*’du 


where </> = .sin 7, u = kx, g{u) = f{u/k). If ^(u) is 
set equal to zero when | u | > kl/2, 

Pi<p) = Pof_y'‘Wrlu- (13) 


This Fourier integi’al relation between the pattern of 
a line source and the shading of the line source cor- 


line of point sources; the method is illustrated in the 
following example. 

5.4.5 Designing for a Gaussian 
Pattern 

Consider the Gaus.sian pattern 

P = (15) 

where (p = sin 7. For small iX this is sharply peaked 
at 7 = 0 and the breadth of the peak increases with 
increasing A. By substitution and integration in equa¬ 
tion (14), 

9(U) - (10) 

2 \/ TT 

It is clear that the source required to give a true 


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118 


DIRECTIVITY PATTERNS 



Figure 18. The pattern of a paraholically shaded line source of length I in terms of the dimensioidess parameter (//X) 
sin 7 . X is tlie wave length of the signal and 7 is the angle between the normal to the line source and the direction of 
olxservation. IF is the ratio of the amplitude at the ends to the amplitude at the midpoint of the line source. 


Gau.ssian ])attem is infinitely liroad, since the etivia- 
tion above gives a nonzero value of ^(u) for all finite 
values of u. However, as u increases above the value 
2 A, g{u) falls very rapidly and the effective part of 
the radiator is quite limited. The question then is 
where the radiator can be chopped off without ma¬ 
terially affecting the i)attern. This can lie answered 
by substituting (/(u) into ecpiation (13) and inte¬ 


grating between the finite limits, say u = ± Ad/2. 
Then 


P{4>) = 



-(Au 


^ ^-WAr- 




-i- 


COS 



C()XFIDENTL\L 








































































KAIHATING SURFACES 


119 


The alteration in the Gaussian pattern introduced by 
cutting off the radiator at u = + kl/2,orx = ± 1 /2, 
is measured by tlie second term of the equation 
al)ove. This term is never larger than 


E 


2 

v 


, pm 

I ^ 

Akl/i 


e ‘'dt = Erfc 



The (piantity 1 — E is tabulated in Jahnke and 
Emde,“ and Peirce.®^ For example, consider the three 


while the height of the minor lobe is 


h = 


E 

1 - e' 


Further, if w is the ratio of the width of the resulting 
major lobe to the width of the major lobe of a uni¬ 
form line source. 






Figure 19. Directivity ratio of a parabolically shaded line source of length / to a signal of wave length X. IF is the ratio 
of the amplitude at the ends to the amplitude at the midpoint of the line source. 


cases in which the minor lobe is required to be 30 db, 
40 db, and 50 db below the major lobe, which means 
that E must be 0.031G, 0.0100, and 0.0032 respec¬ 
tively. Then x 2 • //X • A must have the values 
1.520, 1.821, and 2.084 re.spectively. To illustrate, a 
radiator 3 wave lengths long with 30-db minor lobes 
gives A = 0.323, which is a pattern whose major lobe 
is approximately 38 degrees wide aci'o.ss the 1/e, or 
8.68 db points. 

From the analysis above, a relationshij) may be 
olitained between the amplitude at which the radi¬ 
ator is cut off and the height of the first minor lobe. 
The ratio of the amplitude at the cutoff to that at 
the center of the line source is 



Thus h and w may be considered functions of r and 
are plotted in Figure 20. The above relations for h and 
w hold only when r is small. When r is large, say be¬ 
tween Xo and 1, the shading is close to parabolic 
shading, for which the patterns have already been 
obtained (see Figure 18). These patterns were used 
to get h and w for large r. 

5 .5 RADIATING SURFACES 

Thus far simjile arrays of point and line sources 
have been discussed and it may have seemed that 
undue emphasis has been placed on the patterns of 
such sources, since actual radiators involve vibrating 
surfaces. However, the results on point and line 
sources have much greater applicability than hereto¬ 
fore indicated; in particular, it will be shown that the 
pattern of a flat source in any plane normal to the 


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120 


1)1 KEd IMT V PATTERNS 


surface of the source is the same as the pattern of 
a line source with an api^ropriatelj' chosen line- 
strength function. 

5.5.1 Baffle Conditions 

Three kinds of baffle conditions will be considered: 
( 1 ) that in which the source is set in an infinite-plane 
stiff baffle, ( 2 ) that in which the source is set in an 
infinite-plane release baffle, and (3) that in which 
the source has no baffle. A surface is called stiff if its 
normal ^’elocity is zero and release if the pressure at 
all points of the .surface is zero. 



Figure 20. The relation between the cutoff ampli¬ 
tude, height of first minor lobe, and width of major 
lobe of a Gaussian shaded line .source. 


5.5.2 Nonbaffle Conditions 

The nonbaffle condition also recpiires a word of 
explanation. It is clear that the body of a transducer 
will always act as a self-baffle, so that it is not pos¬ 
sible to escape some sort of baffle condition in any 
ca.se. Such baffle conditions are extremely difficult 
to analyze. J. K. L. MacDonald has considered the 
case in which a vibrating circular disk is .set in the 
end of a semi-infinite cylinder; the cjdinder is .sup¬ 
posed to be an idealized approximation to the body 
of the transducer. He found that when the radius of 


the disk is of the order of X to 4X (with X the wave 
length of the signal) the pattern obtained is the same 
as that in which the disk is set in an infinite-plane 
.stiff baffle multiplied by the factor 3^(1 -f cos y), 
where y is the angle between the direction of obser¬ 
vation and the normal to the disk. This rule has been 
adopted in the following to obtain patterns under 
the nonbaffle condition even when the face of the 



X 


Figure 21. The pattern of a square source of side I 
as a function of the dimensionless parameter (f/X) sin y. 

X is the wave length of the signal and y is the angle be¬ 
tween the normal to the surface of the source and the 
direction of observation. 

transducer is not circular. It places the nonbaffle 
condition between the stiff- and relea.se-baffle condi¬ 
tions, .since the pattern of a radiator in an infinite- 
plane release baffle may be obtained from the pattern 
in a stiff baffle bj' multiplying by the factor cos 7 .-^ 

5.5.3 Patterns 

The patterns produced by plane surface radiators 
are a little more complex than those of line sources. 
This is so because line sources have an axis of sym¬ 
metry (the line itself), whereas plane .sources in gen¬ 
eral do not. In dealing with line .sources the pattern 


C'OXFIDENTIAL 


































































RADIATING SURFACES 


121 




Figure 22. The pattern of a .square of length I for a signal of wave length X. The solid curve is the pattern in a ])lane 
liarallel to a side, the dotted curve is the pattern in a plane parallel to the diagonal of the square. 



-3 

lO / 






was considered only for directions lying in the plane, 
including the line source. In dealing with plane 
sources, on the other hand, the pattern in all direc¬ 
tions must be observed. A complete representation 
reipiires a three-dimensional graph of the pattern. In 
practice only those directions lying in some plane in¬ 
cluding the normal to the active surface will be 
examined at one time. For example, in examining the 
pattern produced by a square radiator, consider first 
the pattern in a plane parallel to an edge, then in a 
plane parallel to a diagonal, and finally the patterns 
in intervening planes. 


The pattern of a plane-faced radiator set in an in¬ 
finite-plane stiff baffle is given by 

P(u) = Pof (17) 

Here dS is an element of the active surface »S; r is the 
vector from an arbitrarily chosen origin 0 in S to dS] 
u is a unit vector in the direction of observation with 
origin at 0, and k is the wave number of the signal, 
that is k = 27r/X, X being the wave length of the 


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122 


DIRECTIVITY PATTERNS 



Figure 23. The total pattern width 2 y of a square source in a plane parallel to an edge; / is the length of a side of the 

square source and \ is the wave length of the signal. The baffle conditions are: --stiff baffle; — — —no baffle; 

-pressure-release baffle. 



Figure 24. Tlie total pattern width 2y of a square source in a plane parallel to a diagonal. I is the length of a side of 
the square source and X is the wave length of the signal. Baffle conditions are indicated in the .same manner as for 
Figure 23. 


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RADIATING SURFACES 


123 


signal. F{r) is the velocity of the element of surface 
dS and may be complex, since portions of ma\’ he 
out of phase. Pq is a normalizing factor. 

Let a rectangular coordinate system be set up 
whose axis is normal to the face of the source and 
whose X and y axes lie in the face of the source. The 
unit vector u has the components cos a, cos /3, cos y, 
where a, d, and y are the angles between the direction 
of observation and the coordinate axes x, y, z, respec¬ 
tively’. Equation (17) can now be written 

P{a, ft 7) = PoJ (18) 



Figure 25. The amplitude pattern of an Isosceles right 
triangle in a plane normal to the hypotenuse in terms 
of the dimensionless parameter (l/\) sin y. I is the 
length of a side of the triangle, X is the wave length of 
the signal, and y is the angle between the normal to 
the source and the direction of observation. 

Consider, for example, the pattern in the x — z 
plane (the plane jS = 90°, cos = 0). By writing 

fix) = J'F(x,y)dy, 

then 



where the proper limits of integration must be taken. 
Comparison with equation (12) justifies the jirevi- 
ous assertion concerning the equivalence of line 
source patterns and patterns of flat-surface sources 
in planes normal to the surface. 


To prove even more, suppose the strength function 
F{x,y) has the form 

p'i^dj) = gi^) hiy)- 

Then equation (18) takes the form 

The first integral is the radiation pattern produced 
by a line source of strength g(x) along the x axis and 
the second is the pattern of a source of strength 
h{y) along the y axis. Since g{x) and h{y) are arbi- 



Figure 26. The pha.se pattern of an isosceles right 
triangle in a plane normal to the hypotenuse in terms 
of the dimensionless parameter (//X) sin y. I is the length 
of a side of the triangle, X is the wave length of the sig¬ 
nal, and y is the angle between the normal to the 
source and the direction of observation. 

trary^ and since the pattern in the x — z plane is de¬ 
termined by g{x) alone and the pattern in the y — z 
plane by h(y) alone, it has been shown that it is 
possible to prescribe the pattern of a flat radiator in 
two normal planes. For example, suppose the same 
Gau.ssian pattern of ecpiation (15) is desired in two. 
planes. Then both g{x) and h{y) must have the form 
of eciuation (16); therefore 

= fikx) f{ky) 

^ ^^-(.Akx,2)^ -(.Aky/2)^ 
dir 

= _e-(Ar/2)^ 

dir 

where r- = x'^ ifl. The source distribution in this 
case has circidar symmetry in the x — y plane- 


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12t 


DIRECTIVITY PATTERNS 



Figcre 27. The directivity ratio D of a flat rectangular source of sides I and w in a stiff baffle. \ is the wave length 
of the signal. 



X 

Figure 2S. The directivity ratio of a flat rectangular source of sides I and w in a release baffle. X is the wave length 
of the signal. 


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RADIATING SURFACES 


125. 



Figure 29. The directivity ratio D of a long rectangular source of length I and width w to a signal of wave length X. 





Figure 30. The pattern of a flat circular source of 
diameter d in terms of the dimensionless parameter 
(d/X) sin y. X is the wave length of the signal and y is 
the angle betw'een the normal to the plane of the 
source and the direction of observation. 


5.5.4 Product Theorem 

Before a discussion of particular patterns is started, 
the product theorem, a general and useful re.sult of 
research on directivity patterns,- .should be stated. 
Consider a number of radiators of the same frequency 
and of identical pattern and orientation in space but 
possibly with different strengths and phases of mo¬ 
tion. Then, if the reaction of one radiator on the other 
is neglected, the pattern produced by the aggregate 
of the radiators is the pattern produced by an aggre¬ 
gate of point sources having the same distribution in 
space and the same strengths and phases of motion 
as the actual radiators, multiplied by the pattern of 
a single radiator. 


5.5.5 Various Sources 

Rectangular Sources 

It is a simple matter to apply equation (18) to 
obtain the pattern of a rectangular source of uniform 
amplitude and phase in a stiff baffle. The x,y coordi¬ 
nate axes are taken parallel to the sides of the rec- 


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126 


DIRECTniTY PATTERNS 




d=2^ 


d=3^ 



d=4A 



Figure 31. The pattern of a circular di.<k of diameter d in stiff (solid curve) and release (dotted curve) baffles. X is the 
wave length of the signal. 


tangle with origin at the center. 63 - putting F{x,y) 
= 1 and Po = l/lw, where I is the length and iv the 
width of the rectangle, it is found that 

/kl \ . (kw \ 

sin I — cos a J sin I — cos d j 


Square Sources 

In a plane parallel to an edge of the rectangle, say 
the length, d = 90°, cos /3 = 0, and cos a = sin y, 
so that 



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RADIATING SURFACES 


127 


By comparison with equation (11) this pattern is 
seen to be the same as that of a uniform line source 
of length I and is shown in Figure 13. Thus all the 
results on uniform line sources and segmented line 
sources of variable strength and progressive phasing 
may be carried over to segmented rectangular or 
square sources. 


minor lobe as a function of the size of the transducer 
(i/X). For this purpose the cuiwes on Figures 23 and 
24 have been tlrawn. The first gives the pattern 
structure of a square in a plane parallel to an edge, 
and the second, in a plane parallel to a diagonal under 
three baffle conditions. It will be noticed that only 
when / 'X < 2 is the effect of the baffle appreciable. 



Figure 32. Total pattern width 2y of a circular di.sk of diameter d to a signal of wave length X. 


If the radiator is a square, in a plane parallel to the 
diagonal of the .square, a = /3 and 

1 

cos a = cos ^ sin y , 

so that 



where d = \/2lis the length of the diagonal of the 
square. Patterns (19) and (20) are plotted in 
Figure 21 against the parameter (l/'K) sin y. The pat¬ 
terns for the particular dimensions I = 2X, 3X, 4X, 
and 5X are shown in Figure 22. 

It is sometimes desirable to study the width of the 
major lobe and the height and position of the first 


A square radiator is sometimes split along a 
diagonal and the two halves pha.sed differently to 
form a .shifted lobe pattern. It then becomesof interest 
to know the pattern of each half of the split square. 
The pattern of one of the halves in a plane per¬ 
pendicular to the diagonal is given by 



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128 


DIRECTIVITY PATTERNS 


where d is the length of the diagonal of the square 
and 7 is the angle between the direction of observa¬ 
tion and the normal to the face of the square; it is 
taken as positive when the direction of observation 



Figure 33. The directivity ratio D of a flat circular 
source of diameter d for a signal of wave length X under 
variou.s baffle conditions. 


makes an acute angle with the source and as nega¬ 
tive in all other ca.ses. The complex time factor is 
assumed to be The pattern of the other half of 
the square is the conjugate complex quantity P*. 
Figures 25 and 26 show the amplitude and phase 
patterns of P plotted against (l/X) sin y, where 
I = 1 /V 2 d is the length of the side of the square. 

The directivity ratio of a rectangular transducer 
with long length (1) and large width (ic) is simply 


D = 


r- 

■iwlw 






(area; 


( 21 ) 


However, when either I or w or both are small com¬ 
pared with X, this formula for D, which is inde¬ 
pendent of baffle conditions, does not hold. 

In Figures 27 and 28 the directivity ratio of a 
rectangidar source when both dimensions are small 
is given under stiff- and release-baffle conditions. 
The directivity ratio when only one of the dimensions 
is small is given in Figure 29. 


Disks 

The pattern of a circular disk vibrating as a piston 
in a stiff baffle can be obtained from equation (18) 


by first changing to jiolar coordinates with the 
origin at the center of the disk. When the shading is 
circularly symmetric, 

Fix,y) = /(r), 

where r- = -f y-, and 

rd/2 

P = 27rPo I /(r)Jo(AT sin 7 ) rdr- 

Here d is the diameter of the disk and 7 is the angle 
between the direction of observation and the normal 
to the disk. ./„( 2 ) is the 7 dh order Be.ssel function of 
argument 2 and is tabulated in Jahnke and Emde.®^ 



Figure 34. The pattern of a parabolically shaded cir¬ 
cular source of diameter d in a stiff baffle in terms of 
the dimertsionless parameter (d/X) sin 7 . X is the wave 
length of the signal and 7 is the angle between the 
normal to the plane of the source and the detection of 
observation, s is the ratio of the amplitude at the edge 
to tlie amplitude at the center of the source. 


When the disk has uniform strength and phase 
(/(r) s 1 ), and if Pq is chosen appropriately, 

/kd \ 



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RADIATING SURFACES 


129 


This pattern is shown in Figure 30, plotted against 
the parameter (d/X) sin 7 . The particular patterns 
when d = 2X, 3X, 4X, and 5X are shown in Figure 31 
for stiff- and non-baffle conditions. The structure of 
the pattern of a circular disk is shown in Figure 32, 
where the width of the major lobe and the position 
of the first minor lobe are shown as a function of d/X 
under three baffle conditions. 



X 

Figure 35. The directivity ratio of a parabolically 
sh.aded circular source of diameter d in a stiff baffle for 
a signal of w ave length X. s is the ratio of the amplitude 
at the edge to the amplitude at the center of the source. 


The directivity ratio of the pattern of a circular 
disk in a stiff baffle is given by 

jm)' 
kd 1 



When there is no baffle or the baffle is pressure re¬ 
lease (the pre.ssure over the .surface of the baffle is 
zero), the expression for D is more complicated. In 
Figure 33 the i) of a circular disk is plotted against 
d/X under three baffle conditions. When the diameter 


of the disk is large compared with the wave length 
of the signal. 



which agrees with the general result of equation 

( 21 ). 

The pattern of a circular disk with parabolic shad¬ 
ing has been computed. The shading function is 

/(r) = 1 - (1 - s)(^j)\ 


where d is the diameter of the disk and s is the ratio 
of the amplitude of vibration at the edge to that 
at the center of the disk. The normalized pattern of 
such a source in a stiff baffle is 

p = ^ , J 1 - s VJsjz) 

1 “b s Z \1 -|- s/ z 

where 


kd . 

z = — sm 7 • 


These patterns for s = 1, 3^, }/i, and 0 are shown in 
Figure 34, plotted against the parameter (d/X) sin 7 . 
The effect of .shading on minor lobe heights and on 
the width of the major lobe is clearly shown. The 
directivity ratio of these patterns and the corre¬ 
sponding patterns when the baffle is release are given 
in Figures 35 and 36. 

Another type of radiator is a circular flexible dia¬ 
phragm fixed at its edges and vibrating in its funda¬ 
mental mode. Patterns for this case are given by 
Stenzel,® who finds that the central lobe is some¬ 
what broader and the minor lobes lower than for a 
uniform piston, as is to be expected. 

Sometimes a circular disk is split along a diameter 
so that the two halves may be phased separately to 
form a shifted lobe pattern. It is therefore of interest 
to find the pattern of a semicircular piston. In a plane 
normal to the diameter of the semicircle, the pattern 
in a stiff baffle is given by 

p _ + i[*^i(^)] 

^ ~ z 


where 


kd . 

z = — sin 7 , 


d is the diameter of the .semicircle, and 7 is the angle 
between the direction of observation and the normal 
to the face of the source. *S„(z) is the nth order 


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130 


DIRECTIVITY PATTERNS 


Struve function (see Jahnke and Emde and 
Watson,who denotes the Struve function by a 
Iroldface H). The amplitude and phase patterns of 
P are shown in Figures 37 and 38. 

Noise Signals 

All the pattern calculations above have been based 
on the assumption that the signal consisted of a 
single frequency. Excitation of a transmitter or 
microphone by a single frequency signal has some 
disadvantage on account of the standing-wave pat- 



X 

Figure 36. The directivity ratio of a parabolically 
•shaded circular source of diameter d in a release baffle 
for a signal of wave length X. .? is the ratio of the 
amplitude at the edge to the amplitude at the center 
of the source. 

tern which may be set up in the surrounding medium. 
To obviate this difficulty, a signal may be applied 
which has a band of frecjuencies with roughly uniform 
amplitude between the two limiting frequencies. This 
would produce a different standing-wave pattern for 
each frequency, so that the observed result is the 
average over the frequency band and hence does not 



Figure 37. The amplitude pattern of a semicircular 
source of diameter d in a plane normal to the diameter 
in terms of the dimensionless parameter (d/x) sin 7 . X is 
the wave length of the signal and 7 is the angle between 
the normal to the source and the direction of observa¬ 
tion. 



fsiNy 


Figure 38. The phase pattern of a semicircular source 
of diameter d in a plane normal to the diameter in tei ms 
of the dimensionless (larameter (d/X) sin 7 . X is the wave 
length of the signal and 7 is the angle between the nor¬ 
mal to the source and the direction of observation. 

have such large fluctuations in space. The directional 
pattern for such excitations is also modified. Since 
the different frecpiencies are not related in pha.se, the 


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RADIATING SURFACES 


131 



Figure 39. The intensity pattern of a line source of 
length I to a signal conststing of a band of frequencies 
from o)] to u!,. Xo is the wave length of the midband 
frequency wo = V'wiw-. and y is the angle between 
the normal to the line source and the direction of ob¬ 
servation. 


intensity rather than the amplitude mirst be aver¬ 
aged to obtain the intensity jjattern: 

F^ = Pi f\ AM |••=| \^du>, 

where A (w) is the excitation amplitude at the angular 
frequency co, P(w) is the pattern of the source as a 
function of w, and Pi is a normalizing factor. For a 
line .source 

I sin 7 \ 


P(co) = 


2 c / 


where c is the velocity of sound. As.sume 

\ if \ \ 0 ^ W1 < W ^ W2 

' “ )o, elsewhere 

Then it is found that 


p5= ' 


- 1 


Ai) 

(7)' 


sin- (TTur) 

r-—-^-h 


(TTur)- 


.S.(27rur) 




where C 02 = rwo, wi = wo r, Xowo = 27rc, and u = (//Xo) 
sin 7 . *Sj(x) is the incomplete .sine integral tabulated 


3 db 6db 10 db 



Figure 40. Directivity ratio D in terms of total pattern widths 5i in degrees between points 3, 6, and 10 db be¬ 
low maximum. 


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132 


DIRECTIVITY TATTERNS 




Figure 42. Radiation admittance of sjihere. 


in Jahnke and Emde.'’^ This pattern is plotted in 
Figure 39 for the cases in which the band width is 
an octave and a half-octave, and the results are 
compared with the pattern of a pure frequency 
signal. It will be noticed that the principal difference 
is a smoothing out of the minima and a slight de- 
crea.se of the maxima. For other radiators, like be¬ 
havior would be expected. 

Directivity Ratios of Given Patterns 

In various instances the directi\’ity ratio of a pat¬ 
tern has already been shown to be a function of the 
tran.sducer (its shape, size, and shading). However, it 
often happens that the.se properties of the tran.sducer 
are known only inaccurately or not at all, though the 
pattern of the transducer may have been measured 
(}uite accurately. It then becomes of interest to know 
the directivity ratio of a pattern as a function of the 
properties of the pattern itself (its type of symmetry, 
width of major lobe, height of minor lobes, and so 
on). 

If there is no sort of symmetry or regularity to the 
pattern, some form of numerical integration is needed 
to obtain the directivity ratio. Actually the pattern 
is seldom known in more than two perpendicular 
planes .so that it is necessary to assume that the 
overall pattern is the product of the two known 
patterns. If the minor lobes are lower than 25 db, the 



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RADIATING SURFACES 


133 




Figure 45. Radiation imjiedance of infinitely long circular cylinder. 


directivity ratio of the pattern is given cpiite closely 

.-i 

D = - hh 10^^ 

2 

where 5i, 62 are the widths in degrees, G db below 
the i:)eak of the patterns in two perpendicular planes. 


In Figure 40 the directivity ratio is given as a func¬ 
tion of the widths 5i, 5<i when measured 3 db, 6 db, 
and 10 db from the peak of the pattern. The 6-db 
case is based on the formula above. A check is 
afforded by comparing the three values of D given 
by the three parts of Figure 40. The average of the 


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134 


DIRECTIVITY PATTERNS 



Figure 46. Radiation admittance of infinitelj' long 
circular cylinder. 


rounding medium. In considering this problem, at¬ 
tention is focused on the action of the force and 
the reaction of the medium on the applied force. 
In general, this reaction depends, in an extremely 
complicated manner, on the disposition and condi¬ 
tion of constraining surfaces (impedance), including 
the active surface of the transducer itself. The prob¬ 
lem can be stated mathematically as a general bound¬ 
ary value problem requiring solutions of the wave 
equation. Except in a few simple cases, it involves 
a knowledge of higher analysis; therefore, the de¬ 
tailed derivations will not be given here. The results 
will be simply formulated in an elementary manner, 
making use of electromechanical analogies. 



three values of D is probably the best value to use. 
A rough correction term to account for orilinary 
minor lobes may be applied as follows: add 3^ db to 
the directivity index given in Figure 40 for each 5 db 
that the minor lobes exceed —25 db. This should 
give the directivity index to within a decibel. 

5.6 RADIATION IMPEDANCE 

5.6.1 Introduction 

If a sinusoidal force is applied to a surface, the 
surface vibrates and radiates sound into the sur- 


5.6.2 Energy Radiated 

The average energ,y radiated from the active sur¬ 
face (T of a transducer is given by 



where p is the sinusoidally varying pressure and v is 
the normal particle velocity of the radiating surface 
at the element of surface da. Re is an abbreviation 
for “real part of” and v* is the conjugate complex 
\'alue of V. Assume the complex time factor of p and 
V to be 6-'“', where w is the angular frequency of the 
\'iliration. 


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RADIATION IMPEDANCE 


135 


5.6.3 Radiation Impedance and 
Admittance 

After writing 

Z = R+jX 

If the face of the transducer moves like a rigid 
piston, that is, with a uniform velocity v, then 

and 

11 

1 

E = Re-p* 1 pda, 

then 


while if the pressure p over the face of the transducer 
is uniform, 


E = -Rvv*, 

2 

E = Re-pJ'v*da • 


E = ^-Gpp-*- 



.01 0.1 1.0 10 

ka 


Figure 48. Radiation admittance of a cylindrical dipole source. 


In the former ease the complex radiation imped¬ 
ance is defined as 


= -fp'i'’, 


and in the latter case the complex radiation admit¬ 
tance is defined as 


Y = — fvd<r- 


Both definitions coincide when both p and v are uni¬ 
form over a and therefore 

]. 

V Y 




Specific Impedance and Admittance 

The quantity Z/a is called the specific radiation 
impedance, and o-F the specific radiation admittance. 
It is usually convenient to plot the real and imaginary 
parts of 

Z = T + jx, 

y ^ 9 - jb, 

z 

2 = —, 
pea 

aY 

y = —■ 

pc 

p is the density of the medium and c the velocity of 
sound in the medium. The pc is commonly called the 


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136 


DIKKCTIVITY PATTERNS 



0.0i 0.10 La IJO HD 


P'lGURE 49. Radiation impedance of circular piston in stiff infinite plane baffle. 



Figure .50. Radiation admittance of circular piston 
in stiff infinite plane baffle. 


specific acoustic resistance of the medium; it has the 
value 42 in air and 150,000 in water when the units 
are grams per square centimeter .second, or bars sec¬ 
onds per centimeter. 

In Figures 41 to 52, the quantities z and y are 
idotted for various radiators. The independent vari¬ 
able is a dimensionle.ss quantity involving the wave 
number k, given by 



X being the wave length of the signal. 


For a PulsatIxVG Sphere 

The radiation impedance and admittance of a 
pulsating sphere of mean radius a are ])lotted in 
Figures 41 and 42. It is seen that a parallel combina¬ 
tion of resistance peer and inductance paa can simulate 
the radiation impedance and admittance where a is 
the mean area of the sphere. 

For a Dipole Sphere 

The radiation impedance and admittance of an 
oscillating dipole sphere of fixed radius o are shown 
in Figures 4.3 and 44. In this ca.se there is again an 
exacth' equivalent circuit which is .shown on the 
graphs. 

For A Pulsating Cylinder 

Figures 45 and 46 show the radiation impedance 
and admittance per unit length of a long pulsating 
cylinder of mean radius a. The inductance required 
in the equivalent circuit in ortler to give a good ap¬ 
proximation for large ka is twice that needed in the 
case of the pulsating sphere. 

For a Cylindrical Dipole 

The radiation load per unit length of a long oscil¬ 
lating cylinder (cylindrical dijDole) of fixed radius a 
with approximately equivalent circuits is .shown in 
Figures 47 and 48. 


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DIRECTIVITY RATIO 


137 



For a Circular Piston 

The radiation, impedance, and admittance of a 
circnlar piston of radius a set in an infinite-plane, 
stiff baffle are shown in Figures 49 and 50. It is evi¬ 
dent that no simple series or parallel combination of 
resistance and inductance exhibits similar frequency 
variation. However, the same parallel combination 
as for the sphere, for which the impedance and ad¬ 
mittance are shown in dashed lines on Figures 49 
and 50, gives a fairly good approximation. 

For a Long, Flat Strip 
The i-adiation load per unit length of an oscillating 
long strip of width 2a set in a large stiff-plane baffle is 
shown in Figures 51 and 52. The approximately 
equivalent circuit is the same as that of a long 
pulsating cylinder. 

For A Radi.ator of Large Dimensions 

In every ca.se above it will be noticed that when the 
dimensions of the radiator are large compared with 
the wave length of the signal, the radiation imped¬ 
ance is resistive and is very closely given by 

R = pea, 

where a is the active area of the radiator. 



Figure 52. Radiation admittance of long strip in stiff 
plane baffle. 

5.7 DIRECTIVITY RATIO 


The intensity of a sound beam is defined as the 
average energy passing through a unit area and is 
given b}' 

I = Re pr*- 
2 

Thus the total energy passing through a surface S is 
given by 



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138 


DIRECTIVITY PATTERNS 


Let lo be the sound intensity a large distance a from 
the source in the principal direction of propagation. 
If the intensity in all directions were h, the average 
energy radiated woidd be 

Eo = Airarlo. 


The directivity ratio D is defined as 


D = 


E 

Eo 


1 



where 5 is a sphere of large radius a centered at the 
radiator. 

When /o is the maximum I, as is generally the case, 
D is a number between 0 and 1. The more directive 
the sound field, the smaller is D. A uniform sound 
field, such as that of a point source, has a D of 1. 

The directivity index d is defined as 

d = —10 logio D db. 

This number has the desirable propert.y of increasing 
with the directivity of the sound beam. 

At large distances from the source the pressure p 
and the normal particle velocity v are related bj' 


p = pcv. 

If the pressure p at a large fixed distance from the 
source, commonly called the pressure pattern of the 
source, is normalized to be 1 in the principal direction 
of propagation, then the directivity ratio ma}- be 
written 



where 11 is a solid angle (dO = dS 'a-). 

By using the expressions previously obtained for 
the average energj' E radiated from the source, it is 
found that 


R 


■iwa-f po 
pc 


D, 


a'G = -iwa^pcy — JD , 


where R is the radiation resistance of a source having 
a uniform velocitj" v and G is the radiation conduct¬ 
ance of a source of area tr exerting a uniform pi-essure 
p. The pressure and particle velocity of the sound 


field at a large distance a from the source in the 
principal direction of propagation are represented by 
Po and Vo respectively. 

The quotients po/v and vo/p that occur in the above 
equations can be evaluated in certain simple cases. 



Figure 53. Directivity ratio of flat-faced transducer 
when dimen.sions are large. 


for example, when the active face of the radiator is a 
flat surface set in an infinite-plane baffle. When the 
source has a uniform velocity v the baffle is assumed 
stiff, that is, the surface velocity of the baffle is zero. 
Then 

^ 

V a\ 

so that 

direr 

R = pca • - • D. 


When the source exerts a uniform pressure p, the 
baffle is assumed to be pres.sure release. Then 


Vo _ cr 
p peaX 


and 

C = J_. iy. 

pea X" 

In either case, when the dimen.sions are large. 



direr 


Figure 53 is a plot of D against a when a is expre.s.sed 
in square wave lengths. 


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Chapter 6 

RADIALLY VIBRATING TRANSDUCERS 


6.1 INTRODUCTION 


Reference has already been made in Chapter 1 (see 
Figure 13) to the early use of the radial vibration of 
a cylindrical shell of magnetostrictive material in the 
generation of sound waves. A mathematical theory of 
the phenomenon appears in Chapter 3. From equa¬ 
tions (16), (16a), and (18) of Chapter 3, the resonant 
frequency of the first radial mode is easilj^ found to be 

where Cm is the velocity of sound in the magnetostric¬ 
tive material and a is the mean radius of the cylin¬ 
drical .shell. Equation (1) is equivalent to saying 
that the lowest resonant frequency of a tube or 
cylindrical shell is the fi’equency at which the wave 
length in the shell material is equal to the mean cir¬ 
cumference of the shell. Hence for a given value of a 
the resonant frequency is independent of the radial 
thickness. 

The shell thickness is, however, an important fac¬ 
tor in determining the sharpness of the mechanical 
resonance as the following elementary analysis .shows. 
It is assumed that internal mechanical resistance and 
damping due to eddy currents are small in com¬ 
parison with the radiation resistance of the water. 
The latter as.sumption implies that at least one di¬ 
mension of the shell is not small in terms of the 
wave length in water of the radiated sound. With 
these simplifying assumptions, the shell may be 
considered a radial vibrator with radiation damping 
PujCu, per square centimeter of radiating surface. From 
equation (15) of Chapter 3 the ma.ss reactance of the 
shell per unit area of radiating surface may be writ¬ 
ten: 

Mass reactance = mco = (2) 



Then 


jt ^TTl 

At re.sonance, w = coq = 27r/o = — • 

a 


bpmCm 

apwCw 


where b is the radial thickness of the shell. 


(3) 


With the values of pmCm and PuiC,„ for nickel and 
water respectively, the appro.ximate equation is: 

Qrnech = 29.6" ’ (3a) 

a 

In thin-walled drawn commercial tubing the radi¬ 
ation resistance is large in comparison with the ma.ss 
reactance, giving low values of Q. Standard 1.5-in. 
nickel tubing has a wall thickness of 0.035 in. The 
computed value of Q = 0.035/0.75 = 0.047. Imped¬ 
ance measurements on transducers made from such 
tubing show no measurable radial re.sonance in water, 
with the result that the response varies only slightly 


p 



Figure 1. Radial and tangential stresses in cylindri¬ 
cal tube. 


with frequency over a wide range. The efficiency is 
correspondingly low, .so that applications of radially 
vibrating thin-walled tubes have been almost wholly 
limited to their use as hydrophones rather than pro¬ 
jectors. Ring stacks, on the other hand, have been 
designed to have a fairly high efficiency over a com¬ 
paratively narrow frequency range and have been 
used extensively for both transmission and reception. 

An inherent virtue of the radially vibrating tube 
lies in the fact that the area exerting pressure on the 
water is increased over that carrying the magneto¬ 
strictive stress by a factor a/b, the ratio of tube radius 
to the wall thickness. This is easily shown by refer- 


CONFIDENTIAL 


139' 







uo 


RADIALLY VIBRATIM; TRANSDUCERS 


ence to Figure 1. Consider a diametral section of the 
tube, subjected to a h 3 Tlrostatic pressure p. Then the 
component of the externally applied force per unit 
length normal to the section is 2ap. This is in equi¬ 
librium with the force due to the stress P over an 
area 2b, so that 

2ap = 2bP 
or 

P _a 
p b 

It is evident that in the radially vibrating tube one 
problem in transducer design, namel.v, that of secur¬ 
ing proper acoustic loading of the vibrating surface, 
is in a measure automatically solved Iw the inherent 
geometrical configuration of the tube. 



A ORIGINAL STRAIGHT HYDROPHONE 


Leakage Flux 
Flux in Nickel 
Nickel tube 
Laminotions 
Wacd Coil Form 
Coil 


Winding ' •' Flux Polh 

B WOOD CORE OF JP-I HYDROPHONE 



w ar II. The development of the possibilities of mag- 
netostrictively driven tubes stems from the pioneer 
work of A. L. Thuras at the New London laboratoiy. 
The present account of the work carried on there is 
taken from the New London report. The original 
report should be consulted for the extremely valuable 
ma.ss of detailed information it contains. 



FREQUENCY IN KC 



Figure 3. D-16 Mark IVE hydrophone (.sensitivity 

given in decibels versus 1 volt per dyne per square 
centimeter). 



Eddy Currents 

C TOROIDALLY WOUND HYDROPHONE 

Figure 2. Types of Xew London tubular hj'dro- 
phones. 

6.2 THIN-W ALLED TUBULAR HYDRO¬ 
PHONES: NEW LONDON DEVELOPMENT 

Except for the earlj' limited use of the thin-walled 
cjdindrical sonic device shown in Figure 13 of Chap¬ 
ter 1, no references to this type of magnetostrictive 
vibrator ajjpear in the literature prior to World 


The earliest interest of the New London group in 
tubular hj'dropliones was in connection with direc¬ 
tional sonic listening devices when they attempted 
to duplicate, with a feasible design in the sonic- 
frequenc.v range, the directional listening patterns 
then availalde in the supersonic range using ciystal 
hA'drophones. However, like most fertile ideas, it 
soon found other important applications, notably in 
the New London expendable buoy [ERSB] lydro- 
phone and the depth charge direction indicator 
[DCDI] hj’drophones as well as in the sound-gear 
monitoring Inalrophones developed at HUSL. H\"- 
drophones of this tvpe range in size from units 5 ft 
and more in length, used in the JP listening s^’s- 
tems,’®- down to midget units with tubes ^ in. in di¬ 
ameter and 1 in. long. 


CONFIDENTIAL 





















































TI1I\-W ALLEI) TUBULAR HYDROPHONES; NEW LONDON DEVELOPMENT 


141 


6 . 2.1 Sonic Listening Hydrophones 

The desired properties of a sonic listening hydro- 
])hone are (1) a broad-band frequency response be¬ 
low 10 kc and (2) a sharp beam pattern with much 
lower sensitivity in the direction of the minor lobes 
than in the direction of the main beam. As already 
stated, the thin-walled magnetostrictive tube meets 
the first recjuirement. The second requirement calls 
for at least one dimension that is se\’eral times the 
wave length in water of the signal. At 5 kc, a fre- 
cpiency well up in the sonic range, the wave length is 
11.2 in. Tubular hydrophones intended for sonic 
listening evitlently must be sizable affairs. 

The earlier hydrophones built at the New London 
laboratory were designed to operate on magnetic 
remanence. For this u.se, it was found that partial 
annealing of hard-drawn commercial nickel tubing 
led to imi^roved efficiency and greater uniformity. 
The annealing schedule adopted after extensive 
experimentation was three hours at 600 C. This 
treatment was found to increase the remanent perme¬ 
ability from 22 (unannealed tubing) to about 30. 
(These values are api)reciably higher than those given 
for 5-mil nickel laminations in Chapter 4. The differ¬ 
ence is probably to be explained by the greater hard¬ 
ness, which is due to the cold working of the thin 
sheets of the HUSL measurements. However, the 
optimum annealing temperature was practically the 
same as that found in the Harvard measurements.) 

Since the remanence anneal was carried out at a 
temperature at which the permeability of the nickel 
varies rapidly with temperature and since annealing 
at this temperature does not fully era.se the previous 
history, nickel tubing so annealed was found to vary 
widely in its properties. For this reason, a method 
was developed for point-to-point measurement of the 
jjermeability of the long tubes used for sonic listen¬ 
ing hydrophones. The elimination of tubes with non- 
uniform permeability was found to be a necessary 
precaution. 

The sensitivity of a listening hydrophone is of 
secondary importance, since the result desired is 
discrimination between water noise and the noise 
whose source is to be detected. An increase in sensi¬ 
tivity cannot increase the detection range, but a high 
sensitivity means that less gain and noise reduction 
are necessary in the listening amplifier. 

The directivity index D plays an important role in 
the performance of a sonic listening device. It de¬ 
termines the ratio of the respon.se to sound coming 


from the direction of maximum respon.se to the total 
response to sound arriving from all directions. Since 
water noi.se is a controlling factor, it is desirable to 
have response to sound arriving in random directions 
that are low in comparison with respon.se in the 
direction of the main lobe. Taken alone, this calls for 
the reduction of minor lobes, which in general can be 
achieved only at the expen.se of an increa.se in the 
width of the main beam. This latter, however, 
decreases the directional tliscrimination, .so that the 



.1 .2 .4 .6 I 2 4 6 10 

FREQUENCY IN KC 



[I 


I 




Figure 4. M-7/CRT-1.A hydrophone (sensitivity 

given in decibels versus 1 volt per djnie per square 
centimeter). 

optimum imttern for a sonic listening hydrophone is 
necessarily a compromise between that for maximum 
variation of response with angle and that for mini¬ 
mum interference from random noise. Fromatheoret- 
ical study of the problem, the authors of theNewLon- 
donreportconcludethatfor aline hydrophone of given 
length the minimum directive index (maximum direc¬ 
tional discrimination) is that given by a uniform 
velocity everywhere on the radiating surface, pro¬ 
vided the contributions from all points of the surface 


CONFIDENTIAL 
























































142 


RADIALLY VIBRATING TRANSDUCERS 


add in phase on the main l^eam. For a line source, 
this latter condition holds at distances several times 
the length of the source. It is stated on theoretical 
grounds that a 5-ft line hydrophone would be ex¬ 
pected to show approximately 6 db greater discrimi¬ 
nation against random noise originating on the 
horizon than would a 15-in. circular piston and 
.should give greater dLscrimination against spatially 
random sound at frequencies below 6,000 c. Above 
this frequency, the 15-in. piston should be better. 
The relative merits of particular patterns, however, 
are dependent upon conditions of use. 


6.2.3 Expendable Radio Sono Buoy 
Hydrophones 

The requirements of this use were (1) cheapness, 
lightne.ss, and ease of construction; (2) nondirection¬ 
ality; (3) ruggedness; (-4) voltage response that rises 
with frequency in the range from 0.1 to 10 kc. 

Since the submerged life of the hydrophone was 
intended to be only a matter of a few hours, protec¬ 
tion against the prolonged action of sea water was 
not needed. The earlier hydrophone developed for 
this use was a nickel tube 3 in. in diameter, 5 in. long 



Figure 5. Toroidal sonic listening hydrophone. 


6.2.2 Construction Types 

The general types of tubular hydrophones de¬ 
veloped at New London are shown in Figure 2. In 
construction A, there is considerable leakage flux in¬ 
side the tube that does not contribute to the hydro¬ 
phone output. Moreover, external leakage at the 
extremities of the core generates eddy currents in the 
tube. In B, the wood core carrying the windings close 
to the inner surface of the tube was found to reduce 
internal leakage and to produce a 6-db rise in the 
sensitivity. When the coil was wound toroidally 
about the tube wall, as shown in C, the eddy currents 
were reduced to the longitudinal currents caused by 
the circumferential flux. In this construction, eddy- 
current losses can be reduced by lamination of the 
tube, a method that cannot be usefully employed 
with the diametral core. 


(Figure 3). The internal construction con.sisted of the 
diametral, magnetically permeable core with wind¬ 
ings as shown in Figure 2A. The core consisted of 
twelve laminations of soft iron totaling about }/i in. 
in thickness, wound with 265 turns of No. 20 double 
cotton-covered wire with an impedance of about 50 
ohms in the sonic-frequency range. 

A later model was of the type shown in Figure 4. 
In this, 120 turns of No. 22 Vinylite-covered wire 
were wound toroidally on a half-hard, open-ended 
nickel tube to an impedance of about 2 ohms. A 
layer of air-cell rubber (pressure release) was in¬ 
serted between the windings and the inner surface of 
the tube to prevent cancellation of sound pressure 
on the outer surface by the sound entering the open 
ends; this was a necessary provision, since the length 
of the tube was not great in terms of the wave length. 


CONFIDENTIAL 




THIN-WALLED TUBULAR IIYDROIMIONES: NEW LONDON DEVELOPMENT 


143 


Although the voltage sensitivity of the toroidally 
wound type was considerably lower than that of the 
earlier model, the improved frequency response to¬ 
gether with the lower impedance resulted in marked 
overall improvement in performance. 

The hydrophone developed concurrently with an 
improved directional radio sojio buoy [DRSB] was 



MESIMOX 

CASTIH* NICKEL •««•» 



NL-124 END CONSTRUCTION 

Figure 6. Section and assembly of XIj- 130 and 
NL-124. 

a folding 2-ft, straight toroidally wound magnetostric¬ 
tion unit. It consisted of two 12-in. nickel tubes, 1^- 
in. in diameter, with a 0.025-in. wall, annealed ior 
three hours at 1100 F. The.se two elements fall into 
a line when the buoy is dropped into the water.''- 

6.2,4 Sonic Listening Hydrophones: 
Production Models 

The first production hydrophone constructed earh^ 
in 1942 was toroidal or doughnut sliaped (Figure 5). 
It consisted of a hard-nickel tube with a 2-in. diam¬ 
eter and 0.035-in. wall, bent into a ring having a 
24-in. internal diameter and initially not completely 
closed. A coil of 100 turns of No. 20 insulated wire was 
fed into the ring. No internal core was used, and the 


large area included gave rise to serious leakage flux. 
In a later development, the windings were forced to 
the inner surface of the tube b}^ means of a flexible 
fibrous core. The electric closure of the ring, the 
easiest mode of construction, resulted in a .short- 
circuited turn producing high eddy-current losses. 
Tests made at the Underwater Sound Reference Lab¬ 
oratories showed that the pattern did not depart ma¬ 
terially from the theoretical pattern of a uniform 
circle of equal size. The open-circuit sensitivity in the 
frequency range from 0.5 to 2 kc was about —110 db 
referred to 1 volt per dyne per sq cm. Listening tests 
conducted on a submarine moving at three to six 
knots at periscope depth gave ranges on surface ships 
of 4 to 5 miles and bearings to within 2 degrees. 



Figure 7. Respon.se of NL-124. 


The unexpectedly high directional j)roperties of 
the device have been explained by the marked 
change in sound quality of a broad band source when 
the hydrophone is swung past the target. Owing to 
differences in the spacing of the maxima and minima 
in the receiving pattern with a difference in fre¬ 
quency, the ([uality as well as the intensity of the 
audible signal changes with the angle. It is a well- 
known phenomenon of hearing that the ear makes 
much finer discriminations in the quality than in the 
intensity of complex sounds. The toroidal hydro¬ 
phone was the first rather than the last word in sonic 
listening hydrophones, but it had .sufficient merit to 
arouse interest in sonic listening as an effective means 
of detection and location of underwater sources of 
.sound. 

Both because of greater simplicity of construction 
and better performance, the straight tube soon re¬ 
placed the toroidal hydrophone. The earlier forms 


CONFIDENTIAL 





































































RADIALLY VIBRATING TRANSDUCERS 


ILI 


used are shown in Figure 2. A later development, the 
NL-130, was the toroidally wound tube with perma¬ 
nent-magnet polarization shown in Figure 6. It con¬ 
sisted of an annealed nickel tube 1^ in. in diameter, 
5^ in. long, with a 0.025-in. wall. A longitudinal slot 
was cut the full length of the tube, in which was 
soldered an Alnico magnet Me X H di. The tube was 
wound toroidally, leaving a gap in the winding in 
which the Alnico strip was centered. The whole as¬ 
sembly was cast in plastic. 


0 



Figure 8. Pattern of 5-ft XL-124 in baffle, series 

aiding 5- to 9-kc noise iiand. 

Before assembly, the polarizing element was mag¬ 
netized by using an electromagnet which gave a flux 
density of about 15,000 gau.sses in the Alnico. Thus 
magnetized, the Alnico yielded a flux density of 2,000 
to 4,000 gaitsses in the nickel. 

An extended investigation was made of materials 
and techniques for casting. Of the large number of 
plastics tried, only one or two proved to have the 
qualities requisite for this application. These are: 

1. Permanently high electric resistance and low 
moisture absorption. 

2. Perfect adhesion to the windings and tube, with 
freedom from voids. 

3. Chemical stability in sunlight. 


4. A proce.ssing techniriue that can be carried out 
in factory production. 

Consideration of the known properties of various 
plastics reduced the field of possibilities to three: 
(1) styrene, (2) methacrylates, and (3) phenol- 
formaldehyde compounds. Experiments eliminated 
the first two. The phenolic chosen, a commercial 
product known as Resinox,"* meets the reciuirements 
of mechanical strength and ease of handling, but its 
specific resistance (10® ohms per cm) is too low, its 


0 



Figure 9. Pattern of 5-ft XL-r24 in baffle, series 
opposing 5- to 9-kc noise band. 

water absorjition (0.1 per cent) is too high, and it was 
judged not to be .sufficiently stable chemically to 
stand indefinite exposure to sea water without a pro- 
tecti\’e coating. This protective coating consisted of 
a polystyrene tulte coated with a black jiolystyrene 
composition. 

The NL-130 was used as a ba.sic unit for the con¬ 
struction of 3-, 4-, and .5-ft listening hydrophones, the 
NL-124 series. The 5-ft units contained ten of the 


“ Cast phenolic Resinox (Monsanto 4200) 100 parts, 
dibutyl phth.alate 6 parts, ethyl phosphoric acid 5.5 parts, 
cured 72 hours at 60 C. Resin and dibutyl phthalate are mi.xed 
together at a temperature of 60 to 80 C, and ethyl phos¬ 
phoric acid is added while mixture is cooling. 


CONFIDENTIAL 
























TIIIN-WALI.F.D TUBULAR HA DROPHONES: NEW LONDON DEVELOPMENT 


145 


NL-130 elements, which were sometimes shaded to 
give lobe reduction or were of uniform winding with¬ 
out taper. Figures 7, 8, and 9 give tj'pical perform¬ 
ance data for a 5-ft model. 

The development and imiii'ovement in tubular hy¬ 
drophones for sonic listening can best be summarized 
by the table supplied by W. B. Snow of the New 



Figure 10. Underwater loudspeaker. 


London laboratory. The numerical values shown are 
the relative sensitivities in decibels averaged over the 
frequency band 0.5 to 10 kc and corrected to a 3-ft 
length and a common impedance; all values refer to 
the first production hydrophone of the HP-1 listening 
system. 

Date Relative sensitivity 

January 1942 

Straight, core wound, hard-drawn 

nickel tube. —11.0 db 

. June 1942 

Production model ring hydrophone; 
internal winding, no core; hard- 
drawn nickel tube. +7.0 db 


September 1942 

Original toroidally wound, straight hy¬ 
drophone; hard-drawn nickel tube, 
without permanent covering. +.5.0 db 

Xovember 1942 

JP-1 straight tube, wood core; hard- 
drawn nickel tubes for installation 
on submarine. 0 db 

October 1943 

Toroidally wound, straight tube; half- 

hard nickel, plastic cast cover. +12.0 db 


February 1944 

XL-124. Straight-tube annealed 
nickel; permanent Alnico magnet, 
toroidally wound; cast in plastic, 
rubber covered. 

June 1944 

Experimental a-c polarized, toroidally 
wound, annealed nickel. 

August 1944 

Experimental hydrophone of NL-r24 
construction with 2V-Permendur 
tube. 


+ 16.0 db 


+22.0 db 


+20.0 db 




100 1000 10,000 
B FREQUENCY IN CPS 


Figure 11. Response and efficiency of XL loud¬ 
speaker for A, transmitting response and B, com¬ 
puted efficiencies. 


6.2.5 UnderAvater Voice Frequency 
Loudspeaker 

A beginning was made at the New London laliora- 
toiy on the design and production of a loudspeaker 
for an underwater communications system operating 
at .sonic frequencies. The low attenuation in this fre- 


CONFIDENTIAL 











































































































146 


RADIALLY VIBRATING TRANSDUCERS 


quency region promised considerably greater ranges 
than could be obtained in a heterodyne system using 
a carrier frequency in the supersonic range. The sonic 
frequency projector could be used in connection with 
the sonic listening gear. Efficient conversion of elec¬ 
tric energy into sound energy over a wide band of 
frequencies requires a loudspeaker with a radiating 
area comparable in its dimensions to the wave length 
of sound in the transmitting medium. Thus, to 
operate in water at voice frequencies, a large trans¬ 
mitter is necessary. The toroidally wound, cylindrical 
hydrophone scaled up in dimensions would best meet 
the requirements; accordingly, the unit shown in Fig¬ 
ure 10 was constructed. It was composed of three 
concentric, fully annealed laminations 0.015 in. thick, 
18 in. long, formed into a cylinder 9.5 in. in diameter. 
The laminations were consolidated with Du Pont 
hot-melt cement. The windings were of No. 16 
formex insulated wire, wound over an inside lining of 
air-cell rubber to neutralize pressures set up within 
the cylinder. The whole assembly was covered by 
BTL with a coating of 60 per cent butyl and 40 per 
cent methyl-methacrylate. With a d-c polarizing cur¬ 
rent of 3.0 amperes, this speaker gave the measured 
characteristics shown in Figure 11. The efficiency is 
seen to be greatest in the frequency range between 
2,000 and 3,000 cycles, which is desirable for high in¬ 
telligibility of speech. To compensate for the lowered 
output at 1 kc, it was recommended that the ampli¬ 
fier circuit be resonated at that frequency, using a 
4-/uf condenser. Although the results with this model 
were very encouraging, the development had not 
been completed at the termination date. 

6.3 HARVARD MODEL.S 

The interest at HUSL in tubular-type transducers 
was focused on two prime objectives. The first was 
the possible development of special transducers for 
sonar use, but this idea was abandoned early in that 
program. The second grew out of a widespread need 
for means of tuning and aligning the projectors used 
in sound-ranging systems. The requirements for this 
latter use are not widely different from those for the 
sonic listening devices in which the New London 
group was interested except for the difference in the 
frequency range in which they were designed to 
operate. The features desired for sound gear monitor 
[SGM] hydrophones are: relatively simple construc¬ 
tion, mechanical ruggedness, smooth frecjuency re¬ 
sponse, a radiation pattern uniform in azimuth, and 


a sensitivity unaffected by mechanical shocks or tem¬ 
perature variation. All these qualities are poten¬ 
tially inherent in the tubular hydrophone. The B-19B 
hydrophones used in the OAX monitor, with a fre- 
cpiency range from 15 to 26 kc, and the B-19H msec! 
in the OCP extended-range monitor, 10 to 70 kc, 
were the end products of this development.**^ They 
were widely used and were manufactured in quantity 
by commercial firms under Navy contracts. 

6.3.1 Early Experiments 

Experimental work on the tubular-type hydro¬ 
phone was begun at HUSL in the first half of 1942. 
Some of the numerous variants of the vibrating tube 
that were tried in the earlier months are shown in 
Figure 12. Results of the measurements on these 
units may be summed up by saying that in general 
they were useful in showing what to avoid in building 
magnetostrictive transducers. At that time the neces- 
■sity for delicacy of mechanical construction was not 
recognized. For example, in the light of later experi¬ 
ence it is easy to .see that soldering the joints of S-1 
was sufficiently bad practice to cause nonuniform 
radiation in a plane at right angles to the axis of the 
cylinder. 

S-4 will be recognized as an elongated version of 
the New London toroidal hydrophone. It was made 
of /^-in. nickel tubing, 18 in. long. The windings were 
without core. With an impedance of 1,000 ohms, 
sensiti\dty was relatively high for this type of trans¬ 
ducer, — 80 db vs 1 volt per dyne per scj cm, but the 
efficiency was low, something like 0.05 per cent. The 
elimination of the short-circuit path in the unbroken 
metal construction of S-4 by the introduction of the 
insulating gaskets shown in S-7 resulted in a threefold 
increase in sensitivity and served to give early empha¬ 
sis to the necessity for avoiding a conducting path 
shunting the windings of the transducer. 

S-6 consisted of four annealed nickel tubes each 8 
in. long and 2 in. in diameter. The four tubes con¬ 
tained three coils. The two middle tubes contained 
one leg of each of two coils while the outer pair con¬ 
tained only the return legs of a single coil. The re¬ 
sponse and radiation patterns of this unit are shown 
in Figure 13. Theoretically, the radial resonance fre¬ 
quency of a tube 2 in. in diameter is 31 kc. The peak 
response shown is at 29 kc, and the sensitivity at reso¬ 
nance transformed to a 5,000-ohm impedance is —86 
db referred to 1 volt per dyne per sq cm. The meas¬ 
ured efficiency was 2.0 per cent, an unusually high 


CONFIDENTIAL 



IIARVARI) MODELS 


147 



Figure 12. Four S-type transducers. 


CONFIDENTIAL 





















































148 


RADIALLY VIBRATING TRANSDUCERS 


value for this type of transducer. The pattern was 
equivalent to the theoretical pattern for a rectangu¬ 
lar flat plate 8 in. high by 4.2 in. wide. Since the effi¬ 
ciency was low and the construction of this type of 
hydrophone did not lend itself to production meth¬ 
ods, further development as a possible projector for 
sonar use was abandoned. It is of interest to note, 
however, that the idea of an array of tubular hydro¬ 
phones with their axes parallel and all lying in the 
same plane was carried out cpiite successfidly in the 
QP projector, developed for measurement use, which 
is described later. 




Figure 13. Pattern and response of four-tube hydro¬ 
phone. 


The S-6 marked the close of attempts to produce 
an efficient, radially \-ibrating, cylindrical projector. 
About the middle of 1942 attention was turned to the 
development of laminated stack transducers for this 
use, and work on tubular hydrophones was concen¬ 
trated on jjroducing a transducer that would meet the 
reciuirements of the overside sound gear monitor. 

6.3.2 B-Series Hydrophones 

Operating on Remanence 

In the early stages, development of laminated 
stack transducers was along lines which were being 
followed at New London in the sonic listening hydro¬ 


phones, using unannealed nickel tubes with internal 
windings operating on remanent magnetization. 

Figure 14 illustrates this development. The lens- 
shaped hydrophone A repre.sents an attempt to realize 
the increased sensitivity that theoretically is possible 
from an increa.sed radius of curvature without an in- 
crea.se in periphery.' The measured performance of 
this unit was disappointing. The frequency response 
was ciuite irregular and the average sensitivity low 
( — 140 db referred to 1 volt per dyne per sq cm) over 
the frequency range from 10 to 50 kc. The straight 
tube witli return winding pa.ssing through a brass 
tube B gave good patterns and a smooth frequency 
resjionse ( — 131 db referred to 1 volt per dyne per sq 
cm, impedance 180 ohms at 20 kc), but it was difficult 
to wind and was not a practical construction for 
open-water use. It found use later in an early form 
of the installed monitor. In C is shown the prototyiie 
of the B-6A hydrophone. It differed from the New 
London straight-tube hydrophones in having a 
quadrant instead of a diametral core of Permalloy. 
Similar units in which sextant cores were u.sed were 
built but showed no marked improvement over the 
cpiadrant or Maltese cross type of core. The large 
brass entl caps were an early and unsatisfactory solu¬ 
tion of the difficulty of sealing the ends of the tube 
and making the cable connections without burning 
the insulation off the windings in the soldering proc¬ 
ess. In B-6A, shown at D, the .soldering problem was 
solved by providing the water seal for the cable con¬ 
nection shown at the top and by making the core 
shorter than the tube, so that the bottom could be 
.soldered in without heating the insulation. The first 
and the final forms of sus])ension rig for the B-G hy¬ 
drophones are shown in Figure 15. In the final form 
soldered joints were completely eliminated by pro- 
\-iding circular grooves in each of the stainless-steel 
end caps. The nickel tube fits in the.se grooves against 
neoprene gaskets, the a.s.sembly being held together 
by the six tie rods shown. This type of mounting has 
proved entirely satisfactory for hydrophones using 
13 ^-in. nickel tubes. The B-6C, .shown in Figure 16, 
was supplied with the early units of the 5D sound 
gear monitor motlel but was sub.sequently replaced 
by the B-19B permanent-magnet type. 

A monitor transducer must be used both as pro¬ 
jector and as hydrophone. The use of a polarizing 
current in a portable monitor is objectionable because 
of the bulk and weight of the I’ectifier and blocking 
chokes needed in the electric circuit. Heavy a-c driv¬ 
ing may alter the .sensitivity of a hydrophone operat- 


CONFIDENTIAL 


























HARVARD MODELS 


119 




Figure 14. Four early units of B series. 


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150 


RADIALLY VIBRATING TRANSDUCERS 


ing on remanence by partially depolarizing the mag- 
netostrictive element. 

In Figures 17 and 18 the sensitivities of a B-GA 
(unannealed) and a B-6B (annealed) hydrophone are 
shown as a function of the polarizing current. It will 
be noted that the sensitivity of the hydrophone with 
the unannealed tube is much less dependent on the 
l)olarizing current than is the one with the annealed 
tube. The effect of a-c driving on sensitivities is 
shown in Figure 17B. 



Figure 15. Two type.s of R-G mount.s. 


Tubular Hydrophones with Permanent 
IMagnet Polarization; B-19 

The foregoing limitation of the tubular hydrophone 
operating on remanence emphasized the desirability 
of permanent magnetization when constancy of re¬ 
sponse is essential. The greater stability of the un¬ 
annealed over the annealed tube was offset by its 
lower sensitivity, which called for greater amplifica¬ 
tion in the monitor amplifier. The annealed tube with 
permanent magnetization proved capable of meeting 
both requirements of greater sensitivity and perma¬ 
nent calibration. 

Two experimental models, B-19 and B-19A, were 
built before the final design for the B-19B was 
adopted. In the B-19, polarization was supplied by 



Figure Hi. H-fiC liydiophoiie. 

20 small Alnico magnets each in. in diameter by 
lyi in. long .set in holes in the solid wood core, which 
carried the windings on its circumference. The tlesign 
of B-19A was identical except that 40 magnets were 
used. The first of the latter type to be built was u.^ed 
for a period of six months as a secondary standard at 
HUSL’s Charles River barge. During this time. 


CONFIDENTIAL 















































































HARVARD MODELS 


151 




Figure 17. Hysteresis and depolnrizing effect of 
driving on B-6 hydrophones. 


































































_ 








































1 






























- ( 
















J 

_ 



















J 










1 





V 

\r 









'3-2-1 0 I 2 3 4 

POLARIZING CURRENT IN AMPS 


hiGURE IS. Hysteresis of annealed tube hydrophone. 

eleven independent calibrations were made using 
BTL’s jn-essure gradient standards. Water tempera¬ 
tures ranged from 5 C to 23 C. Although this hydro¬ 
phone experienced rough handling in field u.se during 
this period, no significant sensitivity variations were 
observed. The increased magnetomotive force of the 
40 magnets in B-19A over the 20 in B-19 produced an 
inci-ease of 12 db in sensitivity, suggesting the possi- 
bilit}' of still further improvement b}" the use of more 



R IN OHWS 

Figure 19. Impedance of B-19 liydrophones. 

permanent magnet material. In the B-19B the sepa¬ 
rate magnets were replaced by two prisms of Alnico 
II, each ^6 in. thick by 1.40 in. wide. Pertinent elec¬ 
tric and acoustic data on B-19A and B-19B hydro¬ 
phones are shown in Figures 19, 20, and 21. The 
higher sensitivity of B-19B, even though it has a 
slightly lower imjiedance, indicates a closer approxi¬ 
mation of the optimum polarization. 

Polarization and Aging of Alagnets. The demag¬ 
netization curve of Alnico II is shown in Figure 22. 
The optimum value of B for magnetostrictive re¬ 
sponse in annealed nickel is between 3,500 and 4,000 
gausses. Experience has shown that a close approxi¬ 
mation of this value gives both maximum sensitivity 
and permanence of calibration. The procedure used 
to obtain this value in the B-19B hydrophone is as 
follows: The Alnico prism is left unmagnetized until 
the core assembly is complete. The core piece is then 
placed between the poles of a large electromagnet and 
a field of at least 2,000 oersteds is applied. A magneto¬ 
motive force of about 10,000 ampere turns per inch 
of air gap is required. By j^roper rheostat control, the 
field is gradually reduced to zero and the core is re¬ 
moved from the air gap of the electromagnet. This 
treatment leaves the Alnico magnetized to full 


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152 


RADIALLY VIBRATING TRANSDUGKRS 


strength, which is too great for maximum sensitivity 
and stability. Partial depolarization is effected by 
connecting the core windings to the outi)ut of a 2.50- 
volt Variac and allowing an a-c current of 7 to 9 
amperes to flow through it for a short time. Care is 
taken to decrease the depolarizing current to zero 
smoothly to prevent the possibility of heavy tran¬ 
sients when the circuit is broken. The field produced 


serie.s-i)arallel across the condensers .serve to remove 
any residual charge. The 10,000-ohm, 4-watt variable 
resistor is a means of adjusting the d-c voltage output 
of the rectifier, and the l-zxf, 1,500-volt conden.ser 
jn’ovides some filtering of the rectifier output. Opera¬ 
tion of the device is as follows: The FG-57 thyratron 
(a slow, indirectly heated cathode type) preheats for 
5 minutes; otherwise, damage to the tube will result. 



10 20 30 40 50 6 0 70 80 90 100 

FREQUENCY IN KC 



FREQUENCY IN KC 



FREQUENCY IN CYCUS 

Figure 20. Sensitivity of hydrophone. 


by the magnet after this treatment should be 200 cgs 
units at a distance of 7.0 mm from the pole face. 

An alternative means of polarizing the Alnico mag¬ 
net is shown in Figure 23. A stock power transformer 
(Thordanson 13R16) .supplies 800 volts of alternating 
current (400 each side CT) to the plates of the 
5R4GY half-wave rectifier tube and also 5 volts to 
filament. A .second transformer (Thordanson 19F83) 
furnishes 5 volts at 4.5 amperes for the FG-57 thyra¬ 
tron filament. Two 0.1.5-megohm, 2-watt resistors in 


After the FG-57 cathode is preheated, the “push 
switch” is closed, lighting the 5R4GY filament and 
applying the a-c plate voltage to the half-wave recti¬ 
fier. The d-c output of the rectifier is utilized as the 
charging voltage of the 150-/if bank of condemsers. 
During the charging time, a voltage drop appears 
across the 20,000-ohm, 10-watt resistor, due to the 
charging current flowing through it. This voltage 
negatively biases the grid of the FG-57 thyratron and 
prevents the tube from conducting. When the 1.50-/jf 


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HARVARD .MODELS 


153 


condenser bank has been charged to a voltage equal 
to that of the power supply, the charging current 
ceases to flow and hence the biasing voltage on the 
thyratron drops to zero. The latter becomes a con¬ 
ductor and discharges the 150-/.if condensers through 
the core winding. The cycle will repeat if the push 
button is held down long enough. 


The variations in receiving response and patterns 
among different units are indicated in Table 1. These 
values were obtained from measurements on 13 hy¬ 
drophones picked at random from 140 made at 
HUSL. 

When the transducer was used as a projector, the 
sound pre.s.sure set up at a distance of 1 meter with 8 



^ 10 20 30 4 0 50 60 70 80 90 100 

Z FREQUENCY IN KC 

o 




FREQUENCY IN CYCLES 

Figure 21. Sensitivity of B-19B hydrophone. 


\’arious safety devices such as interlocks, a short¬ 
ing relay across the condensers, and careful protec¬ 
tion of the output terminals (marked B-19B) should 
be incorporated to protect the operator from the high 
voltages and heavy current built up in the operation 
of the device. 

The dependence of the impedance and the sensi¬ 
tivity on the state of magnetization of the Alnico is 
shown in Figure 24. The upper graphs show the effect 
on the frequency response produced by the applica¬ 
tion of a 4-ampere depolarizing current to a fully 
magnetized core. The lower curve shows the change 
in sensitivity at 20 kc caused by depolarizing currents 
of increasing magnitudes up to 10 amperes. 


volts applied across the terminals varied between 43 
and 51 db above 1 dyne per sq cm over the frequency 
range from 10 to 40 kc. No appreciable change in 
sensitivity was found to result from driving at super¬ 
sonic frequencies up to voltages as high as 20. 

With the cooperation of members of the New 
London laboratory, rigorous tests for possible effects 
of shock waves have been made. A B-19B hydro¬ 
phone was mounted on the deck of a submarine sub¬ 
merged at 100 ft. No measurable change in sensi¬ 
tivity resulted from 16 successive explosions of 300- 
lb depth charges at a distance of 300 yd. 

Construction Details of B-19B Hydrophones. Figures 
25, 26, and 27 give the as.sembly details of the produc- 


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RADIALLY VIHRATINf; TRANSDUCERS 


131 


tion model. The permanent magnet i.s made from two 
cast sections of Alnico II, each 0.312 X 1.40 X 2.5 
in. The core halves are made of wood impregnated 
with phenolic resin and cemented to the magnet. The 
coil consists of 130 turns of No. 2G single cotton- 


frecpiency response and pattern are affected to a con¬ 
siderable degree by the delicacy of mechanical details. 
(Succe.s.sful commercial })roduction of B-19B hydi'o- 
phones for use with the OAX overside sound-gear 
monitor was carried out on a large scale by the 


T.\ble 1. Variations of sensitivity and receiving patterns of thirteen B-19B hydrophones. 


Frequency (kc) 

10 

15 

20 

25 

30 

35 

40 

Sensitivity (db ref. 1 volt/ 
dyne/ciiF) 








Max 

-114 

-112 

-112 

-111 

-111 

-112 

-no 

Min 

-119 

-114 

-114 

-117 

-114 

-114 

-113.5 

Avg 

-116 

-113 

-113 

-114 

-112..5 

-113 

-111.5 

Pattern variation 








Max 


2.0 

3.0 

2.5 

1..5 

2.0 


Min 


0.3 

0.7 

0..5 

0.6 

0.7 


Avg 


1.3 

1.8 

1.7 

1.1 

1.0 




500 400 300 200 100 0 

DEMAGNETIZING FORCE H IN OERSTEDS 

Figure 22. Demagnetization curve of .Vlnico II. 


I3RI6 

(THOROARSON) 5R4GY 



Figure 23. Circuit for jiolarizing magnets. 


covered wire and is wound in two halves on specially 
designed jigs to fit nicely on the wooden core pieces 
to which they are cemented. The whole core as¬ 
sembly is cemented and baked into a compact unit 
that makes a sliding fit in the nickel tube. Both 




P'lGiiRE 24. Effect of partial depolarization on sen¬ 
sitivity of B-19B hydrophone. 


Presto Recording Corporation of New York and the 
Harvey Radio Laboratories of Cambridge.) 

B-19H Hydrophone. The B-19B meets tlie require¬ 
ments of monitor use iqi to 40 kc, apitroximately the 
frequency of the first radial resonance of a 1.5-in. 
nickel tube. Above this frequency, the horizontal pat¬ 
tern is no longer uniform, and the response varies 
widely with the orientation of the hydrophone. The 
B-19H (Figure 28), which is es.sentially a miniature 
reproduction of the B-19B, has a tube and is 

polarized by a Cunico diametral magnet. The reso¬ 
nance frecpiency is 83 kc. Curve 1 of Figure 29 gives 
the .sensitivity of the bare hydrophone. Impedances 
in air and water are shown in Figure 30. The vari- 


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HARVARD .MODELS 


155 


ation in liorizontal pattern was found to be not 
greater than 2.0 db at frequencies from 10 to 70 ke. 

The efficiency of B-19H is relatively low. The 
directivity indices and efficiencies, computed from 
sensitivity data by equation (25) of ChajDter 1, are as 
follows: 

Frequency 20 kc 30 kc 60 kc 

Directivity index 0.225 0.193 0.104 

Per cent efficiency 0.084 0.25 0.36 

In the earliest units the end caps were simply brass 
plugs soldered into the ends of the nickel tube, after 
the fashion of the B-GA type. But when the tube was 



mounted in the lantern-type mount, a sharp irregu¬ 
larity in response, accompanied by a large varia¬ 
tion in the horizontal pattern, occurred at 21 kc, as 
shown on curve 2, Figure 29. The smaller diameter 
tubes of the B-19H proved much more susceptible to 
undesired vibrational modes than were the larger 
tubes of the B-19B. Electric measurements on the 
mounted hydrophone in air (Figure 30) gave no 
evidence of a motional impedance circle at 21 kc. 
This anomalous behavior has not been fully ex- 
))lained, but it involves mechanical coupling between 
the tube and the end caps. Tubes mounted in end 
caps with corprene (cork-neoprene) washers inter¬ 


posed between tube and end cap gave a smooth fre¬ 
quency response, but this type of mount was too 
fragile to be practical. 

After con.siderable experimentation with mounting 
in a protective cage, the production model .shown in 



Figure 26. Preassembly of B-19H. 

Figures 31 and 32 was evolved. The protecting cylin¬ 
der (H) of expanded stainless steel is hydrogen- 
welded to the stainless-steel end rings. The flange of 
the upper end cap (A) is bolted to the upper ring of 
the protective cage, with a corprene washer (!) sepa¬ 
rating the two metal .surfaces. 

The lower end of the tube (B) fits .snugly into a 
ring of butyl nibber (F), which isolates it from the 
protective cage. This method of mounting largely 
eliminates the spurious resonance at 21 kc and re¬ 
duces the .strain on the soldered joint between the 
tube and the upper end cap. Both soldered joints are 
protected from corrosion by painting with Amercoat 


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156 


RADIALLY VIBRATING TRANSDUCERS 


33, a water-resisting polyvinyl-chloride-based paint. 
Soldered joints painted with this material and ex¬ 
posed for 200 hours to hot salt spray showed no sign 
of deterioration. The receiving and transmitting re¬ 
sponse and pattern data for five units presented in 
Figure 33 are typical. 


be used with its long axis lying in the horizontal 
plane, it was designed to have a sharp azimuthal 
pattern. For this reason, the three-coil construction 
proved preferable, since the desired pattern could l)e 
obtained bj^ shading the two half-length sections at 
the end. One half of the circumference of the tube was 



Figure 27. Coil and magnet assembly of B-19B. 





■ 1 . ' 61 ^ ' '■/ • 


Figure 28. Unmounted B-19H hydrophone. 


T.\ble 2. Characteristics of the B-19K hydrophone. 


Frequency (kc) 

5 10 

15 

20 

Impedance 

28 -b /28 33 -b /49 

38 + j70 

43 + /8o 

Sensitivity (db 
vs 1 volt / 
dyne/cm-) 

-112 -110 

-110 

-no 

Field at 1 meter, 
10 volt driving 
(db vs 1 dyne/ 
cm-) 

41 48 

48.0 

48.5 

Horizontal pat¬ 
tern variation 
(db) 

0 4.0 

1.0 

1.0 

Efficiency (per 
cent) 

. 0.12 


0.29 


covered with pressure-release material (air-cell neo¬ 
prene) to control the jtattern in the median plane 
perjiendicular to the axis. When it is used in search¬ 
ing, the h 3 'drophone is mounted in a streamlined 
housing (Figure 35) made of molded Lucite, with pro- 



0 10 20 30 40 50 60 70 80 90 100 


FREQUENCY IN KC 

Figure 29. Sensitivity of B-19H, (1) without mount¬ 
ing and (2) with lantern-type mount. 


Variants of the B-19 Type Hydrophone. Several hy¬ 
drophones of the B-19 t.vpe have been built for 
special uses. The B-19K was built to serve as a pro¬ 
jector for monitor use in the octave from 5 to 10 kc 
to supplement the B-19H, which is unsatisfactory as 
a projector below 13 kc. The oxide-annealed nickel 
tube was 2.5 in. in diameter and 6.5 in. long. In¬ 
ternally it was a 2.5-in. version of the B-19B. Its 
characteristics are shown in Table 2. 

The B-19L (Figure 34) is an 11-in. modification of 
the B-19B and was intended for the use in locating 
submerged stationarj" sound sources. Since it was to 


vision for rotating the hvdrophone about its length. 
Rotation of the transducer with its dome about the 
axis rotates the beam in azimuth. The patterns at 
25 kc in the two jilanes are shown in Figures 36 and 
37. 

A number of B-19H units 2 in. long have been 
built. The.se have proved to be more subject to indi¬ 
vidual variations in response and pattern. Well-be¬ 
haved units, however, showed theoretical^ pre¬ 
dictable characteristics, namehy sensitivities about 
8 db below the 5-in. B-19H and patterns corre¬ 
sponding to the theoretical for a 2-in. line source. 


CONFIDENTIAL 


































HARVARD MODELS 


157 



R IN OHMS 

Figure 30. Impedance of B-19H. 



sati.sfactorily on the USS Galaxy for a period of more 
than a year. 

2. A hollow rubber form reinforced internally with 
expanded metal, with a tubular transducer inserted in 
a cylindrical cavity in the rubber. Difficulty was 
experienced in getting an assembly free from air be¬ 
tween the transducer and the rubber, as well as in 
molding rubber which would be free from voids 
around the expanded metal. One satisfactory unit 
was produced in this waj^ 



Figure 32. Production model B-IOH. 



Figure 33. Transmitting anrl receiving response of 
B-19H. 


Figure 31. Preassembly of B-19H (production 
model). 

6.3.3 Installed SGJVI Hydrophones 

A hydrophone intended to be permanently in¬ 
stalled for monitoring use must be enclosed in some 
form of streamlined housing. Various mountings have 
been tried, which are briefly described as follows. 

1. Thin-walled stainless steel of “teardrop” cross 
section enclosing a B-6A hydrophone. The form was 
filled with outgassed castor oil. Because of poor re¬ 
sponse and patterns, this was replaced by a free- 
flooding housing of expanded metal, covered with 
thin stainless-steel sheet (0.020 in.). This was used 


3. Transducers mounted in the pitometer log 
strut.’’ Several different types of mounting were tried. 
The most successful is shown in Figures 38 and 39. A 
B-19H hydrophone was inserted in a cylindrical hole 
in a rubber casing vulcanized into the window in a 
bronze frame of pitometer log cross section. The effect 
of the bronze casing on sensitivity and pattern is 
shown in Figure 40, but since, in the use intended, the 
orientation of the installed unit relative to the pro¬ 
jector would be fixed, the rather large variation in the 

^ Pitometer log equipment, developed by the Pitometer 
Log Corporation includes a streamlined strut with two 
tubes for measuring the static and dynamic pressure of the 
water. 


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158 


RADIALLY VIBRATING TRANSDUCERS 



THREE - COIL UNIT TWO - COIL UNIT 


Figure 34. listening hydrophone. 

Control for Changing VERTICAL 




Figure 36. Pattern of B-19L in jilane of the axis. 
Solid line, with pressure-release hacking; broken line, 
without backing. 



Figure 37. Pattern of B-19L in plane perpendicular 
to the axis. 


pattern would not rule out this hydrophone for 
monitor use. Four of these units were built and two 
gave satisfactory monitoring service on Navy ships 
for periods of more than six months. 


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HARVARD MODELS 


159 




Figure 38. In.stalled SGM in pitometer log strut. 


6.3.1 Laminated Tube Transducers 

Harvard Experimental Units 

Attempts at HUSL to get higher efficiencies in tulie 
transducers by laminated construction were not very 
successful. Efforts in this direction were limited to 
laminated tubes built of thin nickel stock rolled into 
scrolls or built up in layers, with the successive layers 
bonded together with an adhesive. Sections of several 
types tried are shown in Figure 41. 

The form shown at .4 was made by winding layers 
of nickel sheet 0.003 in. thick on each half of a split 
mandrel to form a double D, giving a diametral core 
on which the coil was wound. Forms at B and C were 
provided with diametral wooden cores with periph¬ 
eral windings. 



Figure 39. Production model of installed SGM 
hydrophone. 


90* AZIMUTH 



.,301-------L. 

10 20 30 40 

FREQUENCY IN KC 


Figure 40. Sensitivity of installed SGM hydrophone: 
(1) unmounted hydrophone, (2) at 90 degrees azimuth, 
(3) at 0 degrees azimuth. 


In B, the magnetostrictive tube was formed by 
winding the thin annealed-nickel sheet on a mandrel 
under constant tension. The scroll thus formed was 
reannealed to remove winding strains and then con¬ 
solidated with adhesive. 


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160 


RADIALLY VIBRATING TRANSDl CER8 


The laminations of the layer-built tubes shown at 
C were annealed and the composite tube was formed 
by placing the first layer on a mandrel and coating it 
with Vinylseal resin. After the coating was partly 
dried, the second layer was applied. The proce.ss was 
repeated until the .seven split tubes had been built 
up into a solid unit. This was placed in a compression 
mold and baked under pressure for half an hour at 
150 C. 


her of cements and consolidating techniques were 
tried in cooperation with the Westinghou.se Electric 
Company’s laboratory in Sharon, Penn.sylvania. The 
methods employed were those used in building split- 
core transformers. A defect, now obvious, in the 
units with wooden cores and peripheral internal 
winding lies in the fact that no advantage accrues 
from the laminated structure. This is due to the mag¬ 
netic shielding of the outer by the inner layers. One 



Figure 41. Cross sections of three types of latniiisted tubes. 



Figure 42. Bell Telephone Laboratories’ MKX lam¬ 
inated scroll hydrophone. 

Six of the .scroll and three of the layer-built tubes 
were made, all 1 in. in diameter and 43/^ in. long. 
None of the.se showed sensitivities as great as that of 
a control unit with a solid annealed-nickel tube 0.035 
in. thick of the same dimensions and wound to ap¬ 
proximately the same impedance. The chief difficulty 
was in getting a uniform mechanical structure. With 
a single exception, the patterns of all the laminated 
tubes were poor. In consolidating the scrolls, a num- 


of the layer-built units was subsequently rewound 
toroidally and gave a re.sonant respon.se with a Q of 
2.8 and a mea.sured efficiency of 20 per cent. All 
things considered, however, the laminated ring stacks 
with toroidal winding presented fewer mechanical 
difficulties and greater promise than the laminated 
tubes. Further development of these tubes was ac¬ 
cordingly abandoned at HUSL late in 1943. 

Rixg Scrolls by Bell Telephone L.\bor.\tories 

An account of work at BTL in the development of 
a nondirectional transducer includes a de.scription of 
a spirally wound ring of Permalloy tape 0.002 in. 
thick and 0.375 in. wide. This was wound to give a 
ring with outside diameter of 2.36 in. and wall thick¬ 
ness of 0.197 in., designed for maximum response at 
24 kc.'**'* The surface of the Permalloy was insulated 
by applying a thin layer of silica by cataphoresis 
while the ring was being wound. The ring was an¬ 
nealed and vacuum-impregnated with bakelite resin. 
It was wound with a layer of cotton tape over which 
was wound a single layer (320 turns) of Xo. 28 
enameled, silk-covered wire and again impregnated 
with bakelite resin, bonding the winding to the ring. 
This construction would be expected to give a much 
more compact a.ssembly than the method used for the 


CONFIDENTIAL 













RING STACKS 


161 


tubes at HUSL. However, the frequency response 
proved to be far from smooth and the pattern in the 
plane of the ring was only fairly uniform. This irregu¬ 
larity, observed in all the tape-wound models, was 
explained by the probable presence of low-frequency 
modes superimposed on the radial mode of vibration. 
An account of later and more successful experiments 
at BTL with specially wound tape rings will be 
found in the final section of this chapter. 

A somewhat unusual application of the radial vi¬ 
brator was made by BTL in the MKX hydrophone 
designed for the transmission of acoustic energy to 
the water through an intervening shell of steel.'® This 
hydrophone is shown in Figure 42. In this ease the 
ring was 0.002-in. nickel tape annealed at 600 degrees 
to operate on a remanent flux density of 3,600 gausses 
and a coercive force of //o = 14 oensteds. The con¬ 
struction of the ring was otherwise similar to that 
just described. A 1.25-in. rubber cylinder with diam¬ 
eter greater than the inside diameter of the ring was 
forced into the ring. The rubber cylinder was 
cemented to the steel backing plate. The latter 
carried a cupped i-im that .served to center the hydro¬ 
phone in the desired position with the free end of 
the rubber cylinder in contact with the inner surface 
of the shell through which .sound was to be tran.s- 
mitted into the water. The backing plate was drawn 
down, compressing the rubber cylinder so that its 
clamped length was about 85 per cent of its free 
height. The radial vibrations of the ring excited 
longitudinal alternating stresses in the rubber that 
were transmitted through the metal .shell into the 
water. 

6.4 RING STACKS 

The ring stack transducer is composed of ring lami¬ 
nations which vibrate radially. In toroidal winding, 
the electroacoustic tran.sformation is effected by the 
magnetostriction of the laminae. The design of a ring 
stack is a fairly straightforward job. If there is me¬ 
chanical uniformity in the plane of the ring, then the 
pattern in this plane will be uniform. Since the mean 
circumference of the stack is one wave length of sound 
at the resonant frequency in the magnetostrictive 
material, and since the wave lengths in water and 
metal are proportional to the velocities of sound in 
the two media, it is ea.s\" to show that the mean diam¬ 
eter of the stack is about 1.1 wave lengths of sound 
at the resonant frecpiency in water. Hence the pat¬ 
tern in a plane containing the axis will be approxi¬ 


mately that of a line source of length equal to the 
height of the stack. The re.sonant frequency and the 
patterns are thus determined by the mean diameter 
and the height of the stack respectively. The me¬ 
chanical Q is given by equation (3) and involves only 
the ratio of the radial thickne.ss to the mean radius. 

6.4.1 Design Features 

The ring stacks built at HUSL were generally de¬ 
signed to have a Q of about 5, which from equation 
(3) calls for the ratio of radial thickness to radius of 
about 0.17. In Table 3 are shown the dimen.sions and 


Table .3. Dimensions of ring dies. 


Nominal 
freq. of 
ring 

stack in 
kc/sec. 

Lami¬ 

nation 

thickness 

(inches) 

ID 

(inches) 

h/u 

OD 

(inches) 

Material die 
was designed 
to punch 

20 

0.010 

2.6.52 

0.22 

3.308 

N iekel 

23.5 

0.010 

2.315 

0.228 

2.745 

Nickel 

24 

0.010 

2.42 

0.167 

2.86 

2\'-Permendur 

26 

0.010 

2.23 

0.172 

2.65 

2V-Permendur 

28 

0.010 

1.94 

0.169 

2.30 

Nickel 

31 

0.010 

1.87 

0.164 

2.20 

2V-Permendur 

36 

0.075 

1.61 

0.171 

1.91 

2V-Permendur 

40 

0.075 

1.42 

0.19 

1.72 

2V-Permendur 

54 

0.005 

1.006 

0.17 

1.194 

Nickel 

58 

0.005 

0.875 

0.16 

1.205 

Nickel 

60 

0.005 

0.97 

0.18 

1.15 

2V-Permendur 


materials of the various ring stacks that were built at 
the laboratory. In general, the measured resonance 
frequencies agreed well with computed values. As 
would be expected, the value of Q shown by measure¬ 
ment of the completed transducer was affected by a 
number of factors besides the ratio of radial thick¬ 
ne.ss to radius. Thus, a stack with the height of a 
wave length or less in water showed a Q higher than 
the computed value because the water loading was 
not wholly resistive, as it was assumed to be in deriv¬ 
ing the formula for Q. Impregnating and plasticizing 
a stack resulted in lowering the resonance frequency 
as well as in reducing the sharpness of the response. 
Experimental stacks with a b/a value considerably 
le.ss than 0.17 were built and showed almost uniform 
respon.se over a wide frequency range. All told, the 
ring stack has proved a quite flexible electroacoustic 
tramsducer. An efficiency of 40 to 50 per cent was 
realized repeatedly with a Q of 5. It was po.ssible to 
build a thin-walled stack of 2V-Permendur with a 


CONFIDENTIAL 













162 


RADIALIA VIBRATING TRANSDUCERS 


thickness-to-radius ratio of only 0.06 and a Q of less 
than 2 that showed a measured efficiency of 15 to 25 
per cent over the frequencj^ ran^e from 40 to 60 kc. 

6,1.2 Thickness and Heat Treat¬ 
ment of Laminations 

As Chapter 3 showed, eddy-current loss is a func¬ 
tion of both frequency and lamination thickness. The 
thicknesses of the laminations used in the ring stacks 
listed in Table 3 will be seen to lie below the critical 
thickness for the various frecpiencies as shown in 
equation (3). Hard, half-hard (600 C), and fully an¬ 
nealed (1000 C) nickel rings have been built, the first 
two designed to operate on remanence, the last re- 
(|uiring d-c polarization. The 2V-Permendur was an¬ 
nealed at 500 degrees for one hour in hydi’ogen. 

The half-hard nickel has lower coercive force than 
the hard but has a higher remanent magnetization 
and greater coefficient of electromechanical coupling. 
After flash polarization either with a heavy d-c or a 
nonoscillatory condenser discharge, ring stacks of 
either hard or half-hard nickel will stand being driven 
at low levels without depolarization. So used, driving 
efficiency as high as 40 per cent has been realized. 
The 2V-Permendur is decidedly superior for ojiera- 
tion on remanent magnetization. It can be driven 
with alternating current giving a depolarizing field as 
great as 12 oersteds without being demagnetized. A 
Permendur stack was driven continuously for half an 
hour at cavitation pressure without being depolarized 
in any measurable degree. 

6. t.3 Consolidations of Stacks 

The con.solidation of ring stacks presents no pai- 
ticular difficulties. In the case of unannealed and 
half-hard nickel and Permendur, the bonding agent 
should provide electric insulation between lamina¬ 
tions. The oxide layer that forms on fully annealed 
nickel serves this ])ui'pose. Numerous cements were 
used succe.ssfully at HUSL, but, on the whole, C-3 
C'ycle-Weld, made by the C'hrysler C'orporation, 
proved the most satisfactory. Cycle-W'eld 55-6 does 
not furnish the neces.sary insulation for nonoxidized 
laminations, although it produces strong stacks, ^'ery 
little difficulty was encountered with parasitic reso¬ 
nances in ring stacks, in contrast with longitudinally 
\ ibrating stacks. In con.solidating with C-3 Cycle- 
A\’eld, the rings are laid out on wire mesh, sprayed on 


both sides, and either air-dried at room temperatures 
for a period of a few fiours or at a temperature of 
120 C' for 20 minutes. They are stacked on a mandrel 
turned accurately to the inside diameter of the ring 
and baked under pressure at a temperature of 320 C 
for 20 minutes. Oxide-coated rings may be stacked 
on the mandrel and 55-6 Cycle-Weld brushed on the 
outer surface of the stack. 

6.4,4 Winding: Turns and Wire Size 

The number of turns and the size and type of wire 
used will depend on the impedance de.sired, the allow¬ 
able d-c resistance, the ease of winding the various 
sizes of wires, and the tyjje of mounting used. The 
impedance is determined by the specific use intended. 
At IIUSL the most commonly usetl value of imped¬ 
ance for ring stacks was apjjroximately 125 ohms. 
Ordinarily, the choice between meeting a specified im¬ 
pedance by either parallel or series tuning was made 
so that the transducer could be wound with the most 
convenient size of wire and number of turns. For ex¬ 
ample, the 24.5-kc 2yVSpherical Source transducer,'"* 
which was made up of stacks in. high, would have 
retiuii'ed a large number of turns of fairly small wire 
if it had been series-tuned to the desired impedance. 
However, when the stacks were wound with about 
140 turns of No. 19 wii-e, an easy size to wind, these 
transducers could be ixirallel-tuned to the necessary 
value of impedance. 

If no ])olarizing current is used, transducers operat¬ 
ing at magnetic remanence can be wound with what 
amounts to only a ijartial layer. Full winding of d-c 
polarized stacks is needed to get 0 ])timum polariza¬ 
tion without burning out the wire. 

The choice between a plastic-covered or an en¬ 
ameled wire was usually determined by the type of 
mounting and by whether or not the toroidal wind¬ 
ings were to be expo.sed directly to the water. If the 
windings were to be ex])osed, plastic-covered wire 
was necessary, but the jdastic covering takes up a 
considerable amount of space, so that many fewer 
tui’ns can be put on than of enameled wire. AIoreo\’er, 
idastic-covered wire is cpiite easily punctured or 
abraded in use. 

Since the d-c resistance of the wire varies invensely 
as the scpiare of the wire diameter, whereas the num¬ 
ber of turns per linear inch varies directly as the 
wire diameter, the total number of ampere turns per 
inch for a given d-c voltage increases with wire size. 
^^4re size was usually determined by the ea.se of 


CONFIDENTIAL 



RING STACKS 


16:5 


winding. It was found that No. 19 enameled wire was 
about the largest size that could be conveniently u.sed 
in most applications. 

A very large number of turns of small wire wound 
on a ring stack tends to tune the transducer electri¬ 
cally because of the distributed capacity of the turns. 
Under these conditions, cable capacity may con¬ 
tribute appreciably to the total imi)edance as meas- 
iired at the cable terminals. For most u.ses low-imped¬ 
ance windings were found to be preferable. 

Top a Bottom END RING 



After the laminations were consolidated and before 
the winding was added, the insides of the stacks were 
lined with pressure-release material, such as corprene 
or Cell-Tite neoprene (made by Sponge Rubber Prod¬ 
ucts Company). Washers of the same material were 
usually cemented to the ends of the stacks to prevent 
any interfei-ence by the windings. A bakelite or Lucite 
end cap of the shape of a half doughnut was added to 
each of the washers. This end cap i)rojected slightly 
over the insiile and outside walls of the stack so that 
when the winding was pulled tight there was no 
danger of the wire being injured by coming into con¬ 
tact with the laminations, nor of the vibrations of 


the ring stack being inhibited by the wire. These 
details can be clearly seen in Figure 43. 

6.4..5 Types of Stack Mounting 

In the first ring stack transducers the windings were 
left exposed to the water. The disad\’antages of this 
procedure have already been noted. The next step 
was to encase t he transducer in a rubber or neoprene 
boot filled with castor oil. This process involved out- 



Figure 44. .\ppiir:itus for oil-filling of tran.'^diicers 
under vacuum. 


gassing of the oil and evacuation of the transducer to 
insure that no air would be trapped in the rubber 
container. The vacuum requirements entailed many 
complications, since the mountings had to be care¬ 
fully constructed in order to maintain a good seal. 
When properly built, however, ring stacks mounted 
in rubber and castor oil gave satisfactory perform¬ 
ance. 


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164 


RADIALLY VIBRATING TRANSDUCERS 



F'igure 45. Section of 60-kc spherical pattern transducer. 


Figure 44 shows the method that was used to fill 
transducers with oil under vacuum. If the transducer 
has two oil connections, the oil should be introduced 
through the lower connection while the upper connec¬ 
tion remains under vacuum. 

The castor oil was passed through a chamber 
loosely filled with rubber chips, thus exposing more 
surface area to the low pre.ssure. This increased the 
efficiency of the outgassing process. While in the 
chamber the oil was heated to approximately 80 C 
by means of a nichrome heating coil wound around 
the outside of the chamber. This heating decreased 
the viscosity of the oil so that it flowed more rapidly 
into the transducer and the many small holes and 
crevices inside. A surplus of oil was taken care of in 
the small reservoir just below the outgassing cham¬ 
ber. 

Many of the ring stacks were mounted in a housing 
consisting of metal supporting parts and a i-ubber 
tubing or boot which was vacuum-filled with oil. The 
boot was usually }/i inch thick and was made of good- 
quality rubber or neoprene. The boots fitted smoothly 
over grooved end caps and were cemented to them 
with a cold-setting rubber-to-metal cement such as 
Vulcalock, Miracle adhesive, or Bostik 410D. 

A junction box was usually provided to avoid the 
necessity for evacuating the cable, which had a po¬ 
rous filler, and to allow for changing the cable without 
removing the castor oil. If the transducer was to be 


dri^’en at high voltages, the junction box was com¬ 
pletely lined with some insulating material such as 
fish paper or empire cloth. 

Figure 45 is a section and Figure 46 a photograph 
of a 60-kc spherical-pattern transducer which was 



Figure 4B. k 60-ke spherical pattern ring stack in 
oil and rubber mounting. 


constructed in this manner. The details of the rubber 
boot and of the junction box can be seen clearly. 

When long ring stacks are mounted in this manner, 
it is usuall,y necessary to increase the strength by 
adding a center rod or pipe. This pipe should be well 
in.sulated from the windings of the transducer. If the 


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RING STACKS 


165 


oil is introduced through this pipe, there must l:>e 
enough holes in the wall to allow free passage of the 
oil. 

If there is good electric contact with the water at 
each end of the rod, then an electrically conducting 
center section and the water form a shorted turn 
around the core. Such a shorted turn alters the im- 
jjetlance of the transducer, reduces the sensitivity, 
and may increase the noise pickup. The difficulty 
may be avoided either by insulating one of the end 
caps from the water or by breaking the center pipe or 
rod and inserting an insulating piece. 

The idea of casting a ring stack in plastic was at¬ 
tractive and a large number of experiments were 
performed to find a suitable casting medium. 


T.\ble 4. Experiments in caating transducers. 


Materials 

Difficulties 

Marblette resin casting 

Too hard and brittle; too high 
a coefficient of expansion. 

Latex rubber dipping and 
baking 

Very unsatisfactory; not wa¬ 
terproof. 

Lucite (methvl methacrylate 
resin) casting 

Resin attacks the wire insula¬ 
tion. 

Lucite monomer impregnat¬ 
ing, then polymerizing 

Very unsatisfactory; reduces 
the Q and the efficiencies. 

Successive dippings in Har- 
vell 612-C (cashew-base) 
varnish 

Very satisfactory; it must be 
coated with a waterproofing 
material. 

Neoprene paint 

Difficult to coat in a sufficient¬ 
ly thick layer and in such 
a way as to prevent air 
bubbles from forming. 


Table 4 gives a synopsis of the various compounds 
tried at HUSL and the difficulties encountered. Of 
these the most promising was ca.shew-base varnish, 
but investigation of it was drojtped because of the 
sui^eriority of phenol-formaldehyde resin. 

A number of ring stacks were cast in phenol-form¬ 
aldehyde resin. The technique employed was essen¬ 
tially the one u.sed at New London in casting the 
tubular listening hydrophones. Usually the casting 
was done in a gla.ss beaker or other container, which 
was later removed by breaking if necessary. The ring 
stack was suspended in the glass container (Figure 
47), and the phenolic (Re.sinox), at a temperature 
between 60 and 70 C, was allowed to run in slowly 
but u.suall.y not under vacuum. When the phenolic 



Figure 47. Illustrating method of plastic casting of 
ring stacks. 



Figure 48. Plastic cast 23..5-kc ling-stack trans¬ 
ducer. 

was poured slowly, no difficulty with entrapped air 
was encountered. The plastic material was allowed 
to polymerize at a temperature of 60 C for 48 hours. 
Figure 48 is a photograph of a 23.5-kc spherical-pat¬ 
tern receiver cast in phenol-formaldehyde resin. 

When wooden molds were used, the inside walls of 
the mold were coated with two smooth coats of 
Amercoat 33 Vinylite so that the casting would not 
adhere to the wood. 


CONFIDENTIAL 












166 


RADIALLY VIBRATING TRANSDUCERS 


The polymerized phenolic resin was sometimes 
made more waterproof by coating with an alkyd 
resin prime coat (such as GE’s Glyptal or American 
C’yanamid Company’s Rezyl) followed with a coat¬ 
ing of polystyrene paint (thick type: 100 parts sty¬ 
rene monomer, 25 parts polystyrene, 1 part benzoyl 
peroxide). This paint sets in 24 hours at 60 C. 

Most of the phenolic (Resinox) cast ring stacks 
were coated with Amercoat 33. This paint was ea.sy 
to apply, had good adhesion to the phenolic, but 
was not particidarl}" tough or resistant to abrasion. 
However, it was so convenient that it was used for 
most of the ring stacks built in this way. Amercoat 
23 is said to be similar l.)ut tougher. 


6.4.6 Four Typical Ring-Stack 
Transducers 

A large number of ring stack transducers were con¬ 
structed during the history of HUSL. Of these, four 
models selected as typical and considered in detail 
are described as follows: 

1. An oxide-annealed (1000 C) nickel ring stack 
made of 0.005-in. laminations; 5.0 in. high, with ex¬ 
posed windings; polarized with 8-ampere d-c current; 
ID = 2.65in.;OD = 3.31 in.; mean radius, a = 1.49 
in.; radial thickness b = 0.33 in.; b/a = 0.22. 

2. Half-hard (550 C anneal) nickel stack 0.625 in. 
high, made of 0.010-in. laminations; cast in Resinox, 


T.\ble .5. Characteristics of four ring stack transducers. 



1 

2 

3 

4 

Impedance at i-esonance 





(a) In air 

30 + j70 

127 + j80* 

720 + j50 


(b) In water 


44 + i270 

125 + j270 

6.0 + ./45 

Resonant frequency (/o) 




59.1 kc 

(a) In air 

20 kc 

24.1 kc 

59.3 kc 

(b) In water 


22.3 kc 

58.0 kc 

56.0 kc 

Q =/n/(/, -A)t 





(a) In air 

60 




(b) In water 

.5.0 

6.4 

2.7 

1.3 

Per cent efficiency 





(a) Potential 

64 

33 

()l 

55 

(b) Computed from impedance 

68 

26 

30 


(c) Computed from acou.stic data 

55 



1.5-25 

Sensitivity at resonance 

Db.s ref. 1 volt/dyne/cm- 

-92 

-102 

— 97.5 

-111 

Patterns 

(a) In plane normal to axis 

Uniform 

Max. var. 3.5 db 

Uniform 

Uniform 

(b) In plane containing axis 

.Approximates line 
source 1 = 0.7X 


Approximates line 
source / = IX 

Approximates line 
source / = IX 

(c) Directivity ratio 

0.28 


0.45 

0.44 


* Impedances of bare transducer. 

t/i and /2 are frequencies 3 db down from resonance. 


All things considered, the plastic casting of ring 
stacks proA'ed a more satisfactory method of jjro- 
tecting the toroidal windings than encasing in rubber 
and castor oil. The casting technique, once mastered, 
is relatively simple and does not require an}^ ma¬ 
chined jDarts for mounting. Only a single water seal 
(for the cable) is needed. The re.sonant frequency of 
the stack is generally lowered a little by thick walls 
of plastic, and at the same time the Q is reduced. 
For many uses, the extended band width more than 
compensates for the lo.ss in efficiency. 


operated on remanence from a 10-ampere flash polar¬ 
ization; ID = 2.315 in.; OD = 2.745 in.; a = 1.29 
in.; b = 0.215; b/a = 0.17. 

3. A 2V-Permendur stack, 1 in. high, half hard 
(500 C anneal), made of 0.005-in. laminations 
mounted in castor oil and rubber; operated on 
remanence from 15- to 20-ampere fla.sh polarization; 
ID = 0.97 in.; OD = 1.15 in.; a = 0..53in. ;5 = 0.09 
in.; b/a = 0.17. 

4. Thin-walled .stack, 1 in. high, 2V-Permendur, 
made from 0.005-in. laminations (500 C anneal) 


CONFIDENTIAL 























RING STACKS 


167 


mounted in rubber and castor oil; operated on 
remanence from 15- to 20-ampere flash polarization; 
a = 0.53 in.; b = 0.030 in.; b/a = 0.056. 

The significant data on these four transducers are 
collected in Table 5. Unfortunately, no direct com¬ 
parison among the different types can be made, since 
the wide variation in the tlifferent uses to which 
these transducers were to be put necessitated eciually 
wide variations in their construction. In Figure 49 



0 20 40 60 80 100 120 

R IN OHMS 

Figure 49. Impedance curves of 23..5-kc ring stack 
before and after plastic casting. 


are shown the impedance curves of the 23.5-kc stack 
in air before casting and in water after casting. These 
curves are not significantly different from similar 
curves taken on bare transducers in air and in 
water. The relatively low potential efficiency of 33 
jier cent deduced from measurements in air before 
casting indicates that the low measured efficiency 
of 26 per cent shown by the cast transducer in water 
is not to be attributed to the casting. The effect on 
the 60-kc 2V-Permendur stack of mounting in castor 
oil and rubber is indicated in Figure 50. 

A comparison of the semsitivities of the two 60-kc 
ring stacks is shown in Figure 51. It .should be noted 
that the thin-walled stack was wound to a much 
lower impedance than the other. This, together with 
its much greater band width, accounts for its lower 
sensitivity. However, analysis of the original data 



R IN OHMS 

Figure 50. Impedance of thick-walled 2V-Pennendur 
ring stack. 



FREQUENCY IN KC 


Figure 51. Sensitivities of thick-walled and thin- 
walled 2V-Permendur ring stacks. 


indicated that the efficiency of the thin-walled stack 
was at least as great as 15 per cent over the entire 
freciuency range from 25 to 70 kc. It was found that 
when this stack was used as a projector, a driving 
voltage as great as 20 volts, corresponding to an 
input power of 1.8 watts, would give an undistorted 
wave form for frequencies above 25 kc. The mag¬ 
netizing field in the stack was about 15 cgs units, and 
it was found that the acoustic power output was 
jiroportional to electric input u]) to a peak driving 
current of 0.8 ampere or about 12 cgs units of mag¬ 
netizing field. This puts an upper limit on the 
electric power input which the 2V-Permendur stacks, 
operating on remanence, will handle without being 


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168 


RADIALLY VIBRATING TRANSDLIGKRS 


subject to variations resulting; from partial depolar¬ 
ization b.v the a-c driving current. Experiments with 
a 23-kc thin-walled stack of the same material sliowed 
that it could be driven continuously at a level that 
would i)roduce cavitation at atmospheric pressure 
without depolarization. However, transients set up 
by the sudden making or breaking of the driving 
current at high levels were found to produce changes 
as great as 18 db in the acoustic power output. 



Figure 52. Xondirpctional ring-stack transducer, 
BTL design. 

The highly desirable qualities of thin-walled stacks 
of 2V-Permendur laminations are offset by the prac¬ 
tical difficulties of building such stacks. The only 
procedure so far developed has been to machine down 
thick-walled stacks after consolidation, a rather deli¬ 
cate and not very satisfactory operation from a 
practical point of view. C’omparison of the 15 to 25 
per cent efficiency of thin-walled, toroidally wound 


stacks with the 0.3 per cent efficiency .shown by solid 
tubes of the B-19 type makes it seem desirable to 
develop further the po.ssibilities of laminated radial 
vibrators with low eddy-current los.ses. 

6.1.7 Nondirectional Ring Stack: 

Bell Telephone Laboratories’ Design 

The mounting developed at BTL for ring stacks 
designed to have an aiijiroximately spherical pattern 
is shown in Figure 52. For a re.sonant frequenc}' of 



e 


Figure 53. .\. New London “tliinihle” hydrophone. 

B. Twenty-eiglil clement perpendieulur arrangement 
of 3-ft hydrophone a-ssembly. 



Figure .54. New London 12 X 12-in. transducer. 


24 kc, the lings were of half-hard nickel 0.004 in. 
thick, with ID of 2 in., OD of 2.75 in., and stacked to 
a height of 1.0 in. The laminations were cleaned, 
coated with silica by cataphoresis, and annealed, 
then vacuum-impregnated with bakelite resin. After 
the curing process, the winding was ajtplied and the 
wound ring was then impregnatetl with the same resin 
and cured. Sound-transparent rubber was cemented 


CONFIDENTIAL 



















































MULTIELEMENT TUBULAR TYPE: NEW LONDON MODELS 


169 



PYgure 55. Riuliation patterns of QP projector at A, 25 ko; B, 40 kc; and C, 60 kc. 


with Tri-ply cement to the outer surface and to the 
top and bottom of the stack as shown in Figure 52B. 
The mounting parts are indicated in Figure 52A. 
Measurements showed that a unit of this type had 
a Q of about 6.0 when used as a projector. The radi¬ 
ation in the plane of the ring was practically uniform 
and showed a maximum departure from uniformity 
of 9 db in a plane passing through the axis. The im¬ 
pedance in water at 24 kc was 46 -|- jl92 ohms. The 
acoustic output was linear with input up to a value 
of 10 watts of electric input power. The reported 
efficiency was of the order of 70 per cent. 


6.5 MULTIELEMENT TUBULAR TYPE: 

NEW LONDON MODELS 

The possibility of fabricating transducers built up 
from an array of small radial vibrators was explored 
both at New London and at HUSL. Figure 53A 
shows two of the thimble hydrophones made at New 
liondon for monitoring use.’^® These consisted of hard- 
nickel cylinders, 1 in. long by ^ in. in diameter, 
toroidally wound, with wood-dowel filling cast in 
plastic cylinders. Directional hydrophones were built 
u.sing large numbers of similar midget elements cast 


CONFIDENTIAL 














































170 


RADIALLY VIBRATINC TRANSDUCERS 



-LEAD 

impregnated t^ING 


Figure 5fi. Section of single element of M-o trans¬ 
ducer. 


in solid plastic. A 28-element array with element 
axes perpendicular to the lenfrth of the as.sembled 
hydrophone is shown in Figure 53B. 

The advantage of this construction over the NL- 
130 type lies in its higher efficiency in the upper sonic 


Figure 54. This was built at the New London labora¬ 
tory for field studies comparing a square array with a 
5-ft straight hydrophone using the same amount of 
sensiti\’e material. It consisted of a bronze box with 
an open side, containing ten permanent-magnet 
tubular elements similar to those u.sed in the NL-124. 
The elements were cast in solid plastic and faced 
with sound-transparent neoprene. The impedance 
and frequency resjionses were roughly the same as 
the NL-124; the directivity in the sonic-frequency 
range was much poorer than for the 5-ft NL-124. 

6.6 QP PRO.JECTOR (HUSL) 

The QP transducer described in Chapter 10 was 
built at HUSL for use as a projector at the measuring 
stations. It consisted of fi^'e B-19H hydrophones 


'v-.c- 


*005 


A 

2V- PERMEND.'JR TAPE 
.002'-^®® THICK 





PLASTIC SPACER 
3-120° APART. 





INSULATED CORE 


Figure 57. Details of construction of magnetostrictive element of M-5 transducer. 


and supersonic range of frequencies. The smaller 
diameter and thinner walls of the midget elements 
make for greater sensitivity and lower eddy-current 
losses in the higher frequencies than prevails in the 
larger, thicker-walled tubes. 

A 12-in. by 12-in. square transducer is shown in 


mounted in a flat arra.y inside an open-faced alumi¬ 
num case. These were connected in series inside a 
junction box at the rear of the case and were para¬ 
bolical ly shaded to reduce side lobes. Impedances 
were in the ratio of 25 to 22 to 13 from the center to 
the outside hydrophones. The back surface and sides 


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RING MAGNETOSTRICTIVE TRANSDUCER BY BTL 


171 


of the case were surfaced with air-cell rubber. The 
radiation patterns at 25, 40, and 60 kc in a j)lane at 
right angles to the length of the tubes are shown in 
Figure 55. It will be noted that at the two lower 
frequencies the patterns are roughly tho.se of a single¬ 
plane surface source with lobe reduction. At 60 kc, 
however, where the distance between the centers of 
the tubes becomes about three-fourths of a wave 
length, the pattern appears as that of a series of 


transducer has i:)roved the most satisfactory of the 
considerable number of projectors used in transducer 
measurement at HUSL. 

6.7 RING MAGNETOSTRICTIVE TRANS¬ 
DUCER BY BTL 

The broad band magnetostriction projector developed 
at BTL may be cited as a further example of the use 


, CORPS ENE 



A. 


Figure 58. .4.s.seinbly of 14-element array in M-5 transducer. 


separate line sources. A .similar situation occurs with 
an array of line sources on the .surface of a cylinder 
with phase retardations to give the directional pat¬ 
terns of a flat .surface. In the case of the (^P, the pat¬ 
tern is also modified by the reflection with change of 
phase from the pre.s.sure-release backing. Receiving 
and transmitting re.spon.se curves are given in Chaj)- 
ter 10. For constancy of respon.se over long periods of 
time, freedom from temperature effects, and smooth¬ 
ness of response over a wide frequency range, the QP 


of vibrating rings in a multielement shan>beani 
transducer.'® The purpose of the assignment of this 
task was to “determine the po.ssibilities of develop¬ 
ing a magnetostrictive transducer for sonar use to 
approach the broad frequency range and efficiency 
characteristics of the Rochelle salt type QBF pro¬ 
jector.” The transducer developed is designated as 
the M-o rmg-type magnetostrictive projector and is 
described in detail in reference 9. 

The operation of this device is essentially chfferent 


CONFIDENTIAL 
























SENSITIVITY, d b VS I VOLT/DYNE/CM 2 


172 


RADIALLY VIBRATI!V(; TRANSDUCERS 


from that of the tubes and ring stacks hitherto con¬ 
sidered, in that radiation of energy occurs from the 
inside surface of the ring. In the earlier models, one 
end of the ring was closed with a pressure-release ma¬ 
terial from which reflection with change of phase 
occurred. In later models, a lead disk was irsed foi¬ 



ls 20 25 30 35 

FREQUENCY IN KC 

Figure 59. Receiving response of M-5. 


closure of this end. The change jn-oduced a measur¬ 
able increase in efficiency. The radial vibration of the 
ring jjroduces a to-and-fro movement of the liquid 
partially enclosed within it, causing it to vibrate 
somewhat like a liquid jiiston, thus radiating energy 
from the open end of the ring. The outer .surface of 
the ring moves against a highly compliant material 
which gives no external acoustic loading. The situ¬ 
ation is thus seen to be just the reverse of the more 
u.sual ca.se in which the outer .surface of the ring is 
acoustically loaded. The essential featui-es of a single 
element are shown in Figure 56. 


The individual magnetostrictive element of the 14- 
element array was a spirally wound ring of vanadium- 
Permendur tape (0.002 X 0.375 in.), insulated with 
a very thin deposit of silica dust and wound upon it¬ 
self to have inside and outside diameters of apin-oxi- 
mately 5 cm and 6 cm respectiveh'. The Permendur 
was heat-treated to give maximum remanent mag¬ 
netization to permit operation at low and inter¬ 
mediate levels without d-c polarization. For driving 



15 20 25 30 35 

FREQUENCY IN KC 


Figure 60. .Souiul pres.sure level at 10 ft generated 
by M-5, input 1 volt. 

at higher levels, a polarizing current of 1 ampere in 
the windings was required. The rings were impreg¬ 
nated with bakelite resin, insulated with cloth tape, 
and wound with silk-covered enameled wire. A pro¬ 
tective sheath was molded over the ring and winding. 
The details of construction are shown in Figure 57. 

The a.s.sembly of the 14-element array of the.se 
rings in a diamond-shaped pattern is shown in Fig¬ 
ure 58. A backing plate of corprene is laid against a 
mounting frame of thin brass. A second .sheet of 
corprene, the core plate, is cemented to this. The 
core plate is ]4: in. thick and has circular holes cut in 
it to accommodate the lead disks that act as the 
bottoms of the resonating ca\'ities formed by the 
magnetostrictive rings. A mounting plate of sponge 
rubber % in. thick is cemented to the core jjlate. 


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RING MAGNETOSTRICTIVE TRANSDUCER BY BTL 


173 


The mounting plate has 14 holes, 2.510 in. in 
diameter, in which the molded rings are loosely 
fitted. Substitution of sponge rubber in the final 
model in place of the corprene mounting plate proved 
advantageous. With the corprene, the rings fitted 
rather loosely in the holes, and shrinking or swelling 
of the corprene caused binding of the rings, resulting 
in poor acoustic characteristics. The compliance of 
the rubber proved to be great enough to offer no 
restraint to the freedom of motion of the rings, and 
the transducer gave acceptable patterns with spacing 
between elements as great as a wave length of the 
radiated sound. In use, the tran.sducer was mounted, 
by means of suitable brackets, in a QBF housing, 
which was filled with castor oil under a slight 
vacuum. 

6.7.1 Consolidation of Spirally 
ound Rings 

Earlier in this chapter, the poor performance of 
impregnated scroll-wound rings was mentioned. This 
resulted from the tendency of radial vibrators of this 
type to develop flexural modes of vibration with two, 
four, or even six nodes. A detailed study of the 
problem at BTL showed this effect to be due, in the 
main, to the relatively large spacing (0.0002 in.) be¬ 
tween adjacent turns of the spirally wound tape. A 
solution of the difficulty was found in a special 
technique whereby this space was reduced to 0.00005 
inch, with adequate insulation maintained between 
turns. By using the improved method of consolida¬ 
tion, the 80 to 90 per cent of rejected rings made by 
the earlier process was reduced to a negligible frac¬ 
tion, and the efficiency was increased by about 3 db. 
Bakelite resin (BR-0014) applied in vacuo was used in 
con.solidating the rings. 

The impregnated rings were wound with 200 turns 
of black-enameled, silk-covered wire, and the wind¬ 
ings were impregnated following the same procedure 
as was used in consolidating the rings themselves. 
The protecting sheath was of phenol plastic com- 
po.sed of 15 per cent cotton flock, 15 per cent wood 
flour, and 70 per cent bakelite re.sin (BR-15055), 
molded about the wrapped coil at a pressure of 600 
pounds per square inch. Forms thus molded with¬ 
stood temperature cycles down to — 40 C without 
crackling and with no impairment of their trans¬ 
mission characteristics. Detailed directions for the 
various processes invoh'ed are given in the BTL 
report. 


6.7,2 Electric and Acoustic 
Characteristics 

The receiving response of the M-5 14-element trans¬ 
ducer with three different terminating resistances is 
shown in Figure 59. The curve for the 600-ohm load 
was measured, while those for the open circuit and 
1,300-ohm load were computed from the 600-ohm 
curve and the impedance data. The dependence of 



Figure 61. Impedance of M-o with tuning condensers 
shown. 


band width on the load resistance is to be noted. 
(Compare with Figure 20 of Chapter 1.) Pkir the open- 
circuit condition, the frequency range Itetween the 
— 3 db points is about 2.4 kc, with a Q of 10, while 
for the 1,300-ohm load the band width is about 6.7 
kc, with a corresponding Q of 4.7. The efficienc}' 
at resonance gi\’en in the report was computed from 
the equation 

EITr = /?r — 10 log .4 — log r -|- 115.9, 
where /C = —58.9 db, open-circuit sensitivity, 

.4 = area in sq cm of equivalent circular pis¬ 
ton = TT X 10.5-, 
r = 2,700 ohms. 


CONFIDENTIAL 




























































171 


RADIALLY VIBRATING TRANSDUCERS 


Tlie efficiency thus computed was —2.7 db, or 53 per 
cent. 

By using the same data and a value —21.1 for the 
directivity index (10 log D), the computed efficiency 
comes out —2.5 db, or 63 per cent. 

The transmitting response of the M-5 is shown in 
Figure 60. Here a band width of 7 kc is shown with 
a nominal Q of 3.9. Impedance curves measured with 
the tuning condensers shown are given in Figure 61. 


r = 3.05 meters, 20 log r = 9.7, 

20 log p = 44, 
log Ei = 0, 

Z, = 2,700 + jl200, 

I Z; I = 2,950 ohms, 20 log | Z,- 1 = 69.4, 
10 log D = -21.1, 

-lOlog/fi = -34.3, 

10 log constant = —70.9, 

Eff (decibels) = —3.2 db, or 48 per cent. 



F'igure 62. Radiation patterns of M-5. In horizontal plane at 25 kc. B. In horizontal plane at 30 kc. C. In ver¬ 
tical plane at 25 kc. D. In horizontal plane, halve.s opposing for BDI operation. 


The computed efficiency of the transducer when 
driven by a 600-ohm generator, as gi\'en in the 
report, was —2.8 db, or 52 per cent. The efficienct' 
at 26 kc may be comijuted from equation (20) of 
Chapter 1, using the following data: 


6.7.3 Radiation Patterns 

Figure 62 gives the patterns in various planes and 
also the pattern when the right and left groups of 
rings are connected opposing for RDI operation. 


CONFIDENTIAL 







































KING MAGNETOSTRICTIVE TRANSDUCER BY BTL 


175 


In the last case, balance between the two halves was 
obtained by a small trimmer condenser placed across 
the left half of the transducer. These patterns indi¬ 
cate that the multiple array of ring-type elements 
radiated sound in the direction of their axes in a 
manner cpiite comparable to a circular piston of 
approximately the same overall area. 

T.\ble 6. Constants of 2V-Perniendur magnetostric- 

tive ring. 


Circuit Definition Value of 

constant or formula circuit constant 


/frf 

Li 

s 

r 

m 

R 

G 

Lm 


Rn. 




Rl 


Ca 


C- 


C. 


L, 


Damped-core re.sistance (ohms) 

4.05 

Damped-core inductance (mli) 

1.27 

Stiffness of ring (dynes/cm) 

2.44 X 10‘2 

Mechanical resistance (ohms) 

0.0155 X 10'- 

Mass of ring (grams) 

62.5 

Water load (mech. ohms) 

3.09 X 10" 

Force factor (dynes/ahamp.) 

3.76 X 10» 

G"- 

Motional inductance— X 10~^ (rnh) 
s 

0.0579 

G- 

Motional resistance — X (ohms) 

r 

9120 

Motional capacity ^ X 10^ (^f) 

0.442 

G'l 

Load resistance — X 10“® (ohms) 

45.8 

Tuning condenser-(yuf) 

w'^Ld 

0.0201 

Cd c„. 
c, + c.'"'’ 

0.0192 

C 

0.000875 


30.6 


6.7.4 Characteristics of Individual 
Rinofs 

The preceding sections constitute little more than 
an abstract of that portion of the BTL report that 
deals with the assembled transducer and its salient 
characteristics. Succeeding sections of the report 
contain technical details of construction both of the 
individual elements and of the assembled transducer. 
The section dealing with the consolidation of the 


vanadium-Permendur tape cores is of particular im¬ 
portance, since it appears that the desired behavior 
of the individual rings and hence of the whole trans¬ 
ducer depends in large measure upon the degree to 
which the core, its winding, and the protecting sheath 
are consolidated into a rigid unit. 

As has been shown to be the case in other multi¬ 
element devices, the realizable efficiency of the com¬ 
bination of rings falls considerably below that of a 
single component. Table 6 is instructive as showing 
the physical and electric characteristics of a spirally 
wound ring of vanadium-Permendur tape 0.002 in. 
thick, as well as the potential efficiency of electro¬ 
mechanical transformation of energy. 

Table 7 gives a comparison of the coefficient of elec- 


Table 7. Compari.son of electromechanical coupling of 
2V-Permendur tape-wound ring with those of crystal 
transducers. 



Co 

c, 

k 

Magnetostrictive ring .1-892 

22 

0.23 

(vanadium-Permendur tape-wound ring) 
Z-cut ADP crystal transducer 

13.5 

0.29 

Y-cut Rochelle salt transducer 

12.5 

0.30 

X-cut quartz-crystal transducer 

133 

0.096 


tromechanical coupling of the vanadium-Permendur 
ring with those of crystals now in use in under¬ 
water transducers. 

The development of the M-5 14-ring projector was 
not carried beyond the laboratory stage. However, 
the work done on it demonstrated the possibility of 
making a beam-radiating projector from an array of 
radially vibrating rings radiating energy from their 
open ends. The chief difficulty inherent in the idea 
seems to be the limitation that the geometry of such 
an array imposes on the radiation pattern. Satis¬ 
factory consolidation of the rings under manufactur¬ 
ing conditions would seem to be the major technical 
difficulty to be expected. Simplicity of design and 
economy in the use of a magnetostrictive material 
that can be operated at fairly high levels on mag¬ 
netic remanence recommend this transducer for 
further development. 


CONFIDENTIAL 















Chapter 7 

LONGITUDINALLY VIBRATING LAMINATED STACKS 


7.1 GENERAL CONSIDERATIONS 

7.1.1 Definitions 

A longitudinally vibrating laminated stack is a 
stack of laminations which vibrates in such a way 
that all the particle velocity vectors are parallel to a 
given line that lies in the plane of the laminations. 
Usually the laminations are longer along one axis 
than any other and usually the direction of the par¬ 
ticle velocities is parallel to this long axis. In nearly all 
cases the laminations are made symmetrical on each 
.side of the principal axis of the particle velocity and 
unsymmetrical on each side of the nodal plane. 

7.1.2 General Types 

Uniform Bars 

Types of Stnictures. Examples of uniform bar types 
of laminated stacks are shown in Figures lA, B, C, 
and D. In the.se ca.ses the stacks are of uniform cross 
section along the principal axis of the particle ve¬ 
locity. In each sketch the position of the nodal plane 
and the direction of the particle velocities are .shown 
for the first mode of free vibration. The direction of 
magnetic polarization should be parallel to the parti¬ 
cle velocity. When the bars vibrate the greatest 
mechanical strain occurs in the region of the nodal 
plane and consequently the windings that surround 
the bars should be centered or concentrated in this 
region to give the maximum linkage with the flux 
that is most effective magnetostrictively. 

Bars of the type shown in Figures IB, C, and D are 
made from laminations formed to a channel-like cro.ss 
section by a die-stamjjing operation. Laminations of 
this type are stiff and easy to handle e\’en though the 
metal is thin. The advantage of the X-shaped cross 
section of the bar .shown in Figure 1C is that the 
high-frequency magnetic flux emanating from the 
edges of the laminations when the bar vibrates mag¬ 
netostrictively is distributed over a greater cro.ss 
section of air path; thus the magnetic reluctance of 
the air-path part of the magnetic circuit is appreci¬ 


ably less than that for the bars shown in Figure lA 
and B. 

To give the optimum mechanical and magnetic 
performance, the dimensions of the bars in the nodal 
plane (lateral) should be .small relative to their di¬ 
mensions along the principal axis (longitudinal); that 



C D 

Figure 1. Some typical forms of laminated magneto- 
strictive bars of uniform cross section. 


is, the bars .should be long and slender. If the lateral 
dimensions were made apjiroximately the same as the 
longitudinal dimension, the natural frequencies of 
vibration in the lateral direction would approach 
those of the longitudinal direction and the two or 
more modes of vibration would become coupled, due 
to the Poisson ratio effect. Such coupled modes of 
vibration could easily cause shifts in the frequencies 
of resonance and spoil all attempts to i laintain close 
frequency tolerances on the vibrating elements. For 
magnetization, long slender bars are also superior 
because the demagnetizing field produced by the free 
magnetic poles at the ends is less than that for bars 
with large cross sections, and the ratio of the area of 
the exposed edges of the laminations to the cross- 
sectional area is greater. Thus the high-freciuencj" 
flux density in the air path adjacent to the exposed 


176 


CONFIDENTIAL 









GENERAL GONSIHERATIONS 


177 


edges of the laminations is less, and as a result the 
reluetance of the high-frequency magnetic circuit is 
less. 

Simide bars of this type cannot be used con¬ 
veniently to couple directly to water or a similar 
acoustic medium because the dimensions of the ends 
of the bars are usually small in comparison to the 
wave length in water, and under these circum¬ 
stances the water radiation impedance has a high 
reactive component and a small resistive component. 
If the end of the bar is used as the radiating face and 
if this face is more than a wave length squaie, the 
water radiation impedance becomes nearly resistive, 
with a walue of pc. Under these conditions the me¬ 
chanical Q for the first mode of vibration of the sys¬ 
tem is TT 2 times the ratio of the pc of the bar ma¬ 
terial to the pc of water. Usually, however, bars of 
this type are attached to pistons or diaphragms which 
present to the water radiating areas larger than the 
cross section of the bar. 



Figure 2. Single uiiiforni bar with a pair of laminated 
.steel return paths for the magnetic flux. 


Frcqiiencies and Modes of Vibration. In the first 
mode of longitudinal vibration of a uniform bar the 
node is midway between the free ends, and the dis¬ 
tance from the nodal plane to each free end is just 
a quarter of the wave length in the bar, hence the 
frequency of resonance is 


In general, the frecpiency in the nth mode of vibra¬ 
tion is 


fn = 


nc 


( 2 ) 


In all these modes of vibration the distribution of 
the jiarticle velocity along the bar is sinusoidal and 
conseiiuently the kinetic energy of the vibrating bar 
is the same as that of a lumjjed mass of one-half the 
total mass of the bar vibrating with the same ve¬ 
locity and amplitude as the free end of the bar. 
(This mass is defined as the effective or eiiuivalent 
mass of the vibrating system and will be designated 
by the symbol M*.) If the cross-sectional area of the 
bar is .1, then the radiation resistance of the water 
against the motion of the end of the bar is A{pc)^ 
and the mechanical Q of the system with this radi¬ 
ation damping is 

_ UnM* _ 2'KfnApL _ {pc)bar . . 

“ .4(pc)„ “ 2.4(pc)„, “ 2 (pc)„ ■ 

Thus the mechanical Q for the ?!th mode of vibration 
is n times that for the first mode. 

The magnetic polarization of single uniform lami¬ 
nated bars can be accomplished by use of a com- 
]5onent of direct current in the windings or by use of 
permanent magnets. The degree of perfection of the 
magnetic circuits is determined by the density and 
distribution of the polarizing flux in the bar and by 
the distribution of the reluctance in the high-fre¬ 
quency magnetic circuit. The polarizing flux should 
be parallel to the direction of the jiarticle velocity in 
the most active magnetostrictive regions and should 
have a magnitude sufficient to develop the maximum 
electromechanical coupling in the magnetostrictive 
material. In a well-designed polarizing flux circuit 
more than half of the total magnetic reluctance 
should be due to that portion of the circuit made up 
of the bar itself. This means that any air gaps in the 
circuit should be short in length and large in cross 
section. The same is true of the high-frequency mag¬ 
netic circuit, and it must be remembered that in this 
circuit eddy-current shielding can contribute a large 
amount to the reluctance. 

The simplest possible magnetic circuit for uniform 
bars consists of the bar itself and the air return path. 
Such a circuit is satisfactory only if the cross-sec¬ 
tional area of the bar is very small in comparison to 
that of the air return path. Some magnetic circuits 
which may be used when the cross-sectional area of 
the magnetostrictive bars is relatively large are illus¬ 
trated in Figures 2 and 7. 

A design is shown in Figure 2 for the magnetostric¬ 
tive bar surrounded by the winding and a laminated- 
steel magnetic return path. This type of element re- 
(juires the use of polarizing current, but the magnetic 


CONFIDENTIAL 





































178 


LONGITUDINALLY VIBKATINli LAIVIINATEI) STACKS 


reluctance for both the polarizing flux and the high- 
frequency flux is relatively low. There are several 
alternative ways in which the return flux path of this 



Figure 3. Uniform burs polarized with direct current. 

type can be constructed. One of the most economical 
would be to make the “half shells” from a nest of 
thin .sheets bent into a shallow U-shaped cross .section. 
This general type is not very practical because of the 
difficulty of keeping the bar mechanically free of the 
eoil and magnetic return assembly. 



Figure 4. Uniform bars polarized with .\lnico V 
pei'inanent magnets. 

Figure 3 shows a simple arrangement in which one 
bar serves as the magnetic return for the other so that 
all parts of the magnetic flux path are active mag- 
netostrictively except the relatively small air gaps at 
the top and bottom ends. These gaps can be made 
ns narrow as the thickness of the coil permits. This 


design is quite satisfactory except for the need of 
jjolarizing current. 

Figure 4 shows a method by which a pair of uni¬ 
form rectangular bars can be polarized with small 
bars of Alnico V or anj'' other similar magnetic ma¬ 
terial which has a coercive force of over 500 oersteds 
and sufficient flux density. In this case the polarizing 
flux path and the alternating flux paths are separate 
at the bottom and top ends of the bars. The polariz¬ 
ing flux goes through the Alnico magnets while the 
high-frequency flux goes acro.ss the air gap in one 
direction at the to]) end and the other direction at the 
bottom end between the exposed edges of the lamina- 



Figure o. Uniform bars polarized with sintered- 
oxide permanent magnets. 

tions. The width of the gap between the two lami¬ 
nated bars is determined by the coercive force and 
flux density of the Alnico magnets and by the amount 
of ])olarizing flux leakage occurring between the two 
bars. In the actual construction of an assembly of 
this type, arrangements must be made to keep the 
two bars mechanically free of the coil and polarizing 
magnet assembly and yet hold them in the proper 
relative positions. The best way is to make the coil 
and magnet assembly into a solid mechanical unit 
and support the bars on this assembly by means of 
cushioning material placed near their nodal regions. 

Figure 5 .shows a pair of uniform bars arranged to 
be polarized with sintered-oxide permanent magnets. 
The very high resistivity of sintered oxide makes it 
})os.sible for the high-frequency flux to traverse it 
without any eddy-current lo.sses or shielding. As the 
reversible permeability of the sintered oxide is only 
1.15, it acts almost as a .simple air gap to the high- 
frequency flux. The cross-sectional area of each of 


C'ONFIDENTIAL 


















































GENERAL CONSIDERATIONS 


179 


the sintered-oxicle blocks (measured in a j^lane pei- 
pendicular to the direction of the flux through it) 
should be 4 to G times the cross-sectional area of one 
leg, and the thickness of magnets from the N pole 
lace to the S pole face should be adjusted so that the 
demagnetizing force on the magnets is less than 500 
oersteds when the flux density in the magnetostric- 
tive material is up to the optimum value. To give a 
numerical example as an illustration, suppose the 
bars are made of oxide-annealed nickel, that the fre- 
(piency of resonance is 28 kc, the width of the lami¬ 
nations is one-twelfth their length, and the nickel 
must be polarized to 4,000 lines per scj cm. Then the 



Figure 6. Single bar polarized with longitudinal jicr- 
manent magnets. 

length must be 3.5 in., the width about 0.3 in., the 
height of the magnets about 1.25 in., and the thick¬ 
ness of the magnets about 0.188 in. This leaves 1 in. 
of the center portion of the stacks available for the 
coils. This would be a fairly practical design. 

Figure 6 shows a design in which a single uniform 
bar is polarized Ity means of long rod-shaped Alnico 
magnets placed parallel with it. It is nece.ssary to 
l)revent the magnets from rubbing against the vi¬ 
brating parts of the stack. The magnets should also 
be surrounded with sleeves of thin-walled copper 


tubes or heavily electroplated with copper to prevent 
any a))))reciable amount of alternating flux from tra¬ 
versing the magnets. The best magnet material for 
this application is Alnico V. The coil surrounds the 
entire stack and magnet a.ssembly. The high-fre¬ 
quency flux return is through small packets of thin 
silicon steel laminations cemented to the outside of 
the coil. These j)ackets should be j)laced as far as 
possible from the polarizing magnets to prevent them 
from drawing an excessive amount of polarizing flux 
and thus losing a con.siderable amount of their re¬ 
versible permeability. 

There are many possible variations of the design 
indicated in Figure 6. An example is the alternative 
bar-and-magnet cross section sketched in the lower 
right-hand corner of Figure G. Whatever the vari¬ 
ations ma.y be, it is es.sential that the expo.sed edges 
of the laminations point outward so that the high- 
frequency flux can leave the inner laminations with¬ 
out having to cross through the outside laminations, 
with the consequent eddy-current .shielding. 

Figure 7 shows a design in which the alternating 
flux path is enclosed entirely within the polarizing 
flux path. The polarizing flux is produced by radially 
polarized Alnico magnets which are placed in the 
annular spaces between the laminated bar and the 
steel tube which serves as the return path for the 
flux. The solid copper rings placed at each end of the 
coil assembly serve as high-frequency flux .shields to 
prevent the flux from going to the regions beyond 
the ends of the coil. This design is inherently strong 
and compact. All the parts can be readily supported 
on the steel tube housing. 

Simple Bars with Pistons or Diaphragms 

Types of Structures. Any of the simple uniform bars 
shown in Section 12 can be attached to a piston or 
diaphragm of some kind. Each bar may be attached 
to its individual piston or a group of bars may be 
attached to a single large piston or diaphragm. If two 
or more bars are to operate together in the same 
transducer, all must satisfy the usual jihase and fre¬ 
quency tolerance reciuirements so that they vibrate 
together in close enough unison to give good acoustic 
patterns. 

The active area of the piston associated with a 
single bar is generally made several times as great as 
that of the cross .section of the bar. This allows a 
greater radiation resistance for each bar and conse¬ 
quently a lower mechanical Q, if the ma.ss of the 
piston is not too great. The greater area of the jiiston 


CONFIDENTIAL 























180 


LONGITUDINALLY VIBRATING LAMINATED STACKS 


also allows room around the sides of the magneto- 
striotive bar for the coil, the flux return paths, and in 
some cases the polarizing magnets. Thus the active 
faces of the pistons can present a continuous large 
active face to the water without crowding the mag- 
netostricti\-e bars and their auxiliary parts exces¬ 
sively. 



Figure 7. Uniform l):ir polarized by radially polar¬ 
ized ring-shaped .\lnico magnets, with alternating flux 
path enclo.sed entirely within the ])olarizing flux path. 

The attachment of the laminated bars to the pi.s- 
tons or diaphragm presents some difficult practical 
problems becau.se each lamination must be attached 
perfectly to give satisfactory results. Some of the ma¬ 
terials which have been used for pistons and dia¬ 
phragms are steel, brass, bronze, aluminum, mag¬ 
nesium, polystyrene, molded bakelite, and bakelite- 
impregnated gla.ss fiber. Soft or hard solders may be 
used to attach the bars to steel, bra.ss, or bronze. 
Some of the ^’arious strong thermosetting cements 
are usually best for attaching bars to aluminum, 
magnesium, or plastic diaphragms. An alternative 
method is to solder the laminated bar to a thin steel 
button and cement the flat face of the button to the 
diaphragm. The button may also be made with a 
short threaded stud which screws into a threaded hole 
in the diaphragm. 


Supporting the coil and magnets in a practical 
transducer of this type also presents some difficult 
de.sign jiroblems. The two most successful methods 
are, first, to support them on .some compliant ma¬ 
terial (such as CTll-Tite neoprene), which is cemented 
to the laminated stack in the nodal region, or, .second, 
to support them by a compliant member from the 
piston or diaphragm. Illustrations of these methods 
will be given later in Section 7.2.2. 

Modes and Frequencies of Vibration. When a mass 
is attached to the end of a uniform bar the positions 
of the nodes are no longer symmetrical with respect 
to the bar. In general, the nodes are shifted toward 
the weighted end and the frequency of any given 
mode of vibration is lower than that for the corre¬ 
sponding mode in the bar alone. 

If the thickne.ss of the piston is le.ss than one-eighth 
of a wave length of .sound in the jiiston material and 
if the piston is stiff in a flexural .sense, then it may be 
considered as a lumped mass M The freciuencies of 
resonance occur when the mass reactance of this 
lumped mass is the conjugate of the stiffness react¬ 
ance of the uniform bar at the point of attachment. 
Figure 8 shows a sketch of a uniform bar with a face 
mass attached at one end and graphs showing quali¬ 
tatively the distribution of jiarticle velocit}- and me¬ 
chanical reactance along the length. The cross-sec¬ 
tional area of the laminated bar is cr and the distance 
from the free end is x. The mechanical reactance is 

2ir/ 27r/ 

jpca tan —X = j2Trfm tan —x (4) 

c c 


where m is the mass of a length of the bar, which is 
1 27r times the wave length in the bar material. The 
condition for resonance is' 


j2TrfM L + j2Tvfm tan 



c 


or 


^ 2irf^ Mj. -27rfAU 

tan —L = -= - 

c rn pea 


(fi) 


The values of /„ which satisfy this erpiation are the 
frequencies of resonance. If nii and mi repre.sent the 
values of m for the first and second modes of vibra¬ 
tion respectively, the ratio of the particle velocity at 
the free end of the bar to that of the active face for 
the first mode is 



= sec kjj = 



(fi) 


CONFIDENTIAL 









































GENERAL CONSIDERATIONS 


1«1 


and for the second mode is 



sec k^L 



(7) 


where A;i — 'livfi/c axidkn = 27r/2/c are the wave num- 
liers or radians of phase angle per centimeter of length 
of the bar. 

Radiation Loading and Q's. If the area of the radi¬ 
ating face is .4 and the extent of the face is gi-eat 
enough so that the impedance of the water load is al- 


NOCe FOR m=l 



} GRAPH OF 
VELOCITY 
DISTRIBUTION 


GRAPH OF 
► MECHANICAL 
REACTANCE 


Figure 8. Fundamental vibrational characteristics 
of a uniform bar mass-loaded at one end. The cross- 
sectional area of the laminated bar is cr. 


Magnetic Circuits and Polarization. The magnetic 
circuit and polarization details of elements of this 
ty])e are almost identical with tho.se for the .sym¬ 
metrical uniform bar discussed above. The only im¬ 
portant difference is in the position of the nodes in 
the vibrating bar. The position of the magnets and 
coils should be made to center as clo.sely as possible 
around the primary node. If it is intended that the 
units l)e used at either of the first two modes of vi¬ 
bration, the coil assembly should be shifted slightly 
toward the free end of the bar to include as well as 
possible the node of the first mode of vibration and 
the node nearest the free end for the second mode of 
vibration. 

Double or Multiple Bars with Symmetrical 
Closed Ends • 

Types of Structures. Several lamination forms of 
this type are illustrated in Figui’e 9. All the forms ex¬ 
cept that .shown in D have perfectly closed magnetic 
circuits and consecpiently give the highest possible 




most purely resistive, then the radiation resistance 
for each bar is pc A dynes per cm per second. The 
eiiuivalent mass of the bar for the «th mode of vi¬ 
bration is 

“ sec'^ knL\^k„L .sin knL cos knlL\ (8) 

and the total equivalent mass is this plus the mass of 
the face. Thus 


— M 4 —~ sec’ knL\_k,J-‘ T 'Sin kuL cos k,jP\ • 

(9) 


Consequently the Q for the nth mode of vibration is 
27r/ nM'n 


Qn 


pc A 


( 10 ) 


and this is roughly proportional to n Ijecau.se 4/,* 
remains almost ecpial to one-half the mass of the bar 
for all the modes of vibration. 



Figure 9. Typical forms for laminatetl bars with 
symmetrical closed ends. 


electromechanical coupling coefficients for the jiar- 
ticular magnetostrictive material used as a longi¬ 
tudinal vibrator. However, these forms must be 
polarized by the magnetic remanence flux alone or 
with the aid of a component of direct current in the 
windings. The form shown in D is arranged to be 
polarized by sintered-oxide permanent magnets. The 
advantage of this form is that it can use coils 
preformed over the magnets and slipped into the 


CONFIDENTIAL 





































































1»2 


LON(;iTUI)INALLY VI»RVTIN(; LAMINATED STACKS 


slots. The other forms must be wound l)y threading 
wire back and forth through the winding slots. 

Laminations of this tyjje are punched from fiat 
sheets with good dies .so that a negligible burr is pro¬ 
duced. The thickne.ss of the flat sheets from which 
the laminations should be punched is determined 
by the revei’sible permeability, the re.sistivity, and the 
frecpiency of operation. Reference to Figure 5 of 
C'hapter 3 can be made to select a lamination thick¬ 
ness that gives a characteristic frequency fc, which 
is well above the range of frecpiencies at which the 
tran.sducer is to be u.sed. For example, if the mate¬ 
rial is oxide-annealed nickel, 0.010-in. material is sat- 
i.sfactory up to 25 kc, 0.005-in. material up to 00 kc. 

Modes and Frequencies of Vibration. The most im- 
I)ortant mode of vil)ration is the first, in which the 
one node is at the center as shown in Figure 9. This 
mode of vil)ration is perfectly symmetrical, .so that 
the particle velocities at the two faces are equal in 
amplitude and oi)posite in direction. The .second 
mode of viljration is .sometimes of jn-actical impor¬ 
tance; it is not symmetrical anti the particle velocities 
of the two opposite faces are in the same direction 
and have the .same amplitude. It is relatively easy to 
calcidate the characteri.stics of the first mode of vi¬ 
bration but the .second mode is more complicated, 
since some of the lamination forms anti some of the 
cases retjuire .sjjecial analytical treatment. Therefore 
the di-scussit)!! here will be limited to the first mode 
of vibration. 

Frequencies for forms A, B, and C of Figure 9 may 
be calculated in the same way, since the.se forms are 
essentially alike. At the fretiuency of resonance, the 
reactive component of the mechanical impedance at 
the node is infinite and at the active face is zero. If 
the distance measured from the node is denoted by 
.r, the reactive mechanical impedance per unit height 
of pile-up of stack is 

jpc2w cot kx, (11) 

where k = 2Trflc, as before. 

If the distance measured from the active face in¬ 
ward toward the node is x', the reactive mechanical 
impedance is 

jpeb tan kx'. (12) 

At resonance the.se reactances must be equal at the 
junction between the leg portion and the face por¬ 
tion. Therefore, 

2rrf,/L\ 2rrU 

2w cot-1 -1 = 6 tan- ij (13) 

c \2/ r 


is the relationship between the princijjal dimensions 
and the frequency of resonance. This is a transcen¬ 
dental equation which can be sol\'ed gi-aphically or 
by .succe.s.sive approximation to any degree of ac¬ 
curacy desired. 

AVith X and x' u.sed to denote the same variable 
distances as al)ove, and the rms paidicle \'elocity at 
the active face denoted by Vo, the particle velocity in 
the face section is 

v' = cos A'lx', (14) 


and that in the leg portion is 


V 


Vi) cos k)y 



sin k)X . 


(15) 


Therefore the kinetic energy of the leg .section (on 
one side of the node) pei' unit height of stack is 


ivpvf cos- kiy 


k) .sin- A’ll — 

\ 9 . 



(16) 


and that of the face .section is 


bpvf 


[A, 2 / -t- (.sin A, 2 /)(co.s Aq!/)]- 


(17) 


It follows that the eciuivalent ma.ss of both halves of 
the lamination per unit height of the stack is 


M* = 


2u'p co.s- k'ly 


A'l sin- Aql 


'L\l 

, ‘7 





+ + (sin A-, 2 y)(cos Aq;/)], (18) 

ki 


and, as before, the mechanical Q due to full re.si.stive 
water radiation loading is 


Q 


2^fuM* 

bpc 


(19) 


Magnetic Circuits and Polarization. The magnetic 
circuits and i)olarization of laminated stacks of this 
type will not be considered further here except to 
point out that the thickening of the .sections at the 
centers of the legs of the lamination form shown in 
D of Figure 9 serves two purposes; first, it improves 
the magnetic circuit, and second, it improves the 
electromechanical coupling by mo\ ing the I’egion of 
maximum mechanical strain from the node to the 
junction of the slender leg with the thickened center 
section where the polarizing flux is parallel with the 
direction of the strain. 


CONFIDENTIAL 













GENERAL CONSIDERATIONS 


18.1 


Double or Multiple Bars with Symmetrical 
Closed Ends and Attached Diaphragm 

Stacks of any of the lamination types sliown in 
Figure 9 can tie attaclied to a metal or plastic dia¬ 
phragm. If the diaphragm material has a pc which is 
consideralily greater than that of water and if the 
diaphragm thickness is less than one-eighth of a 
wave length of sound in the diaphragm material, it 



ACTUAL ELEMENT EQUIVALENT FORM 


Figure 10. Element of a laminated stack of double 
uniform bars with symmetrical closed ends and at¬ 
tached to a thin diaphragm of different material. 


may he considered as an additional lumped mass on 
the face. If the thickness of the diaphragm is consid¬ 
erably greater than one-eighth wave length, it must 
be considered as an elastic part of the vibrating sys¬ 
tem. In general, it is good practice to keep the dia¬ 
phragm as small in mass as possible con-sistent with 
maintaining its flexural stiffne.ss. For this rea.son it is 
preferable to make the diaphragms from light mate¬ 
rials such as aluminum alloys, magnesium alloys, or 
certain stiff plastic laminates. There may be rare 
cases in which high Q’s are desired and in which the 
diaphragm should be made ma.ssive and thick in the 
direction of \ ibration. Recent experiments indicate 
that .some interesting modes of vibration and un¬ 
usual frecpiency responses can be obtained from 
laminated stacks attached to relatively thick dia¬ 
phragms of materials of low density. The possibilities 
of vibrating systems of this kind should be explored 
rather thoroughly in the future. 

The problems of attaching the laminated stacks to 
the diaphragm are essentially the same as those for 
laminated uniform bars, which have been discus.sed 
in this .section; the problems of supporting the wind¬ 
ings and polarizing magnets are usually not difficult. 
The coils and magnets u.sually can be attached to the 
laminated stack itself through thin compliant layers 
of material, .such as C'ell-Tite neoprene. 


Modes and Frequencies of Vibration. The simplest 
ca.se to consider is the first mode of vibration of a 
.system of the type shown in Figure 10 in which the 
face .sections attached at each end of the legs may be 
considered as lumiied masses. In such a case 


and 


cot kjji 


cot kiLi 


kiM ^ 

'2p\wh 

kiMi 
- > 

2piwh 


( 20 ) 


where h is the dimension jierpendicular to the plane 
of the laminations, where 


Ml = pibyh, (21) 

M2 = hb{piy -F P22), 

and where ki = 27r/i/ci is the wave numbei’ for the 
freciuency of the first mode of vibration. Therefore, 



serve to determine the length of the legs when the 
frequency, leg width, and face mas.ses are specified. 
The inverse problem of finding the frequency when 
the dimensions and face ma.sses are given may be 
soh ed by finding the solution to the transcendental 
equation 


k = 


1 

Z 


tan-‘ 


2piwh 

kMi 


+ tan~^ 


2p\wh 

ZmZ- 


(23) 


by graphical or successive aiiproximation methods. 

The ratio of the velocity of the back face to the 
velocity of the active face is 


V\ sin k\Li 
Va sin kiL 2 

The effective ma.ss of the system is 


M* = 


sin- kiLi ., piwh 

. „ , -.-Ml + - . „ , . ■ 

.Slid kiL2 ki -sm- kiL2 

[kiLi — (cos kiLi) (.sin fciLi)] + M 2 


(24) 


(25) 


+ 


ki 


Piwh 
siiF kiL2 


IkiL., 


(cos/qTo) (sin A-.Lo)]- 


If the active face is large enough to allow full resistive 
radiation loading and if internal mechanical damping 
is negligible, then the mechanical Q of the system is 

2wfM* 

bh{pc}„ 


CONFIDENTIAL 

































181 


LONGITUDINALLY MHRATINT; LAMINATED STACKS 


If the face portions of the laminations are con¬ 
siderably thicker than one-eighth of a wave length 
and if the diaphragm is also very thick, the modes of 
vibration become so numerous and complicated that 
no attempt at a general analysis of them will be made 
here. As was pointed out above, a con.siderable amount 
of theoretical and experimental research work should 
be done on vibrating systems of this kind. 

The magnetic circuits and polarization of elements 
of this type are the .same as those for the .symmetri¬ 
cal laminations without mass-loading diaphragms, 
except for a .shift in the position of the nodes. 

Double or Multiple Bars with Uxsymmetrical 
Closed or Nearly Closed Ends 

Types of Structures. Several laminations of this 
type are .shown in Figures 11 and 12. Those iiiAand B 
of Figure 11 have legs of uniform width that are paral¬ 
lel,whereas the others have legs of uniform width (e.x- 
cept for the center portions of the legs of B in Figure 
12) that converge towai’d a common center. Tho.se 
with converging legs find application in cylindrical 
.sonar transducers. Several kinds of transducers with 
plane faces have been constructed using stacks made 
of laminations of the general forms indicated in A and 
B of Figure 11. The depth of the heavy end portion 
may vary from about one-eighth wave length to over 
one-rjuarter wave length in the lamination material. 
Hence this part acts as a compres.sible bar, not as a 
lumped mass. 

The problems of stacking, consolidating, mount¬ 
ing, and making provision for acoustic contact with 
the water are the same as for the other types already 
discu.s.sed. 

Modes a?id Frequencies of Vibration. Laminated 
stacks of this type are capable of vibrating in many 
ilifferent modes. The most important of these modes 
in actual cases are the first two longitudinal ones. 
In the discussion that follows, the details of only the 
first mode of longitudinal vibration of laminations of 
the type .shown in A and B of Figure 11 will be pre- 
.sented. The frequencies of re.sonance and the me¬ 
chanical Q's of laminations of the general form shown 
in Figures 11 and 12 when vibrating in the second 
mode are roughly twice those for the first mode. 

Figure 1.3 shows a simplified equivalent form of the 
two-legged laminations which will be used as a liasis 
for design considerations. In practical designs b is 
u.sually of the order of a half wave length in water at 
the desired frequency, w and y are made approxi¬ 


mately and 2ir is made equal to or le.ss than b. 
The exact selection of values of y, iv, IF, anti Ls de- 
pends largely on the value of the mechanical Q de¬ 
sired. For the .sake of clearness, three special ca.ses 
will be considered, (1) where the node lies in the thin 
leg .section, (2) where the node lies at the junction of 


ACTIVE FACE 



c 


ACTIVE FACE 

S ? 


B 

ACTIVE FACE 

TnT 

W ^ 



D 


Figure 11. Types of laminations consisting of two or 
more uniform bars with unsymmctrical closed ends. 


the thin legs and the wide backing section, and 
(3) where the notle lies in the thick backing section. 

Case 1: Node in the thin leg .section. The condi¬ 
tions for resonance are 


tan k\y tan A'lLi 


b ’ 


tan A'lLs tan A'lLo 


ic 

if’ 


(26) 


CONFIDENTIAL 














































<;KNER VI. CONSIDERATIONS 


185 


where ki = 2-n-fi/c as before. If the rms particle ve¬ 
locity of the active face is Vo, then the velocity in the 
face portion is 


= Vo cos kix', (27) 

where x' is the distance from the acti\’e face, the 
particle velocity in the slender leg section is 

^ , cos A’lW . , 

v(xi) = Vo- —Sin A’lXi, (28) 

sin A'lLi 


where the distance Xi is measured from the node and 
is considered positive in the direction of the active 
face. The particle velocity in the thick leg portion is 
given by 


cos A’ly sin A'lLo 

v(xs) = -Vo -—— -r— cos A- 1 X 3 , 

sm A'lLi cos A’li.s 


(29) 


where Xo is the distance measured from the free end 
of the thick leg section. From this distribution of 
jiarticle velocity the effective mass of the vibrating 
.system referred to the velocity of the active face is 
found to be 


M* = p/i |^[A'iy + sin kiij cos A'ly] + 


cos- kiy 
sin- kiLi 


w 

k,' 


[_kiL — cos kiLi sin A'lLi — cos kiL^ sin A’lLo] 


, cosU-ii/ .silF A’lLz TIV, , , . , r , r 

H—^ T + Sill kiLo cos kiLoji • 

//.> A’, ' 


sin- kiLi co.S” kiLs A’l 
The mechanical Q is therefore 

27r/iM* (pc) lam jl 


(30) 


Qi = 


(pc)„. 6 /i (pc)„ 

w cos'- kiy 


) + -sill kiy cos A’l^] 


+ r-w 


[A’lL — cos ^•lLl sin kiLi — cos- 


kiLi sin kjji] -f 


b siiT kiL 

IT cos- kiy sin^ A^Lq 


b sin- kiLi cos'- kiLo 


CA’iLs 


sin kiLz cos kiLo]j • (31) 


Case 2: Node at junction of the thin leg section and 
the thick backing section. In this case the conditions 
for resonance are 

2w 

tan A’ly tan kiLi = , ^.^ 2 ) 

tan kiLz = 00 . 

The second condition means simply that the heavw 
liacking section should be just one-ciuarter wave 
length long. The distribution of particle velocity in 


active face 




Figure 12. Riiig-sluiped laminations whicli are e.ssen- 
tially longitudinally vibrating bars with un.symmetrical 
clo.sed end.s. 



Figure 13. Equivalent form for laminations of the 
form shown in .4 and B of Figure 11. 


the front half of the lamination is the .same as in 
case 1 above. The particle velocity in the thick back¬ 
ing {lortion is 

, , w cos kiy 

v(^3) = -^0—-. — —coskiXz, (33) 

II sm A'lLi 


where X 3 is measured from the free end of the thick 
.section. The effective ma.s.s referred to the velocity 
of the active face is 


M* 


, ) b , • , 7 n , kiy w 

pk '^—lkiy -f- .sm kiy cos hy] -J- 


sin'- kiLi ki 

K'- I 


Ikih - cos kill sin A’lLJ + — , ITL 31 • (34) 

II ^ siiT A'lLi } 


CONFIDENTIAL 
























































186 


LONGITl niNALLY VIBRATING LAMINATED STACKS 


The mechanical Q is 

/I (P^)lam)lp, I • 7 7 11^' 

Qi = , ' ) 7 yLhy + sin kiy cos kiyj + -• 

(pc) a, U 0 


cos^ kjy 
sill" kiLi 


QA'iLi 


cos kiLi sin kjji'] + 


w-Lski cosH'i?/) 

- ( ■ (3o) 

Wb sin- A'lLi ' 


Case 3: Node in thick hacking; section. In this case 
the condition for resonance in the first mode is 


tan kiLz w 

tan ki{L + Jo) Ik ’ 



(3()) 

(37) 


If the particle velocity at the active face is Vu, then the 
particle velocity at the free end of the heavy backing 
section is 


(^ 3)0 


cos kiy cos ki{L + -Co) 
cos kiXo cos kLs 


(38) 


The effective mass, referred to the particle velocity 
of the active face, is 

ohib ^ cos'^ A'lV 

M* = — 

A'l (2 co.s- kiXo 


COS" ki{L + Xo) 


+ 


COS" k'lLz 

cos^ kiy 

- h 

COS" kiXo 


II j^A'iZ/s T sin k\Lz cos k\C^ 


[kiL + sin A'i(L + xo) cos ki{L + Xo) 


sin A’ia:o cos AiXo]| > (39) 


and the mechanical Q is 

(pc) lam 1 

(pC)a> b 1 


„ (pc)lam 1 1 . I \ 

Qm = - 71-1-1-j't 


(40) 


where the brace is the same as that in ecpiation (39). 

The mechanical mounting and the magnetic polar¬ 
ization of laminated stacks of this type can be made 
essentially the same as those for the types discussed 
earlier in this chaiiter. 


Double or Multiple Bar with Unsymmetrical 
Closed Ends and Diaphragms 

In some types of transducers that use unsymmet¬ 
rical laminated stacks it is de.sirable to use a strong 
diaphragm plate for mechanical strength. In these 
cases it is usually desirable to cement the active faces 
of the stacks directly to the diaphragm in order to 
make good acoustic contact and the diaphragm be¬ 
comes a definite part of the vibrating system and 
consequently influences its vibration characteristics. 




A B 



C 


ACTIVE FACE 

D 

Figure 14. Miscellaneous forms of laminated longi¬ 
tudinally vibrating transducer elements. 



The complete theory of the modes of vibration of 
systems of this type has been worked out, but the 
results of the few experimental models constructed 
indicate that some unusual mechanical filter action 
occurs, giving ri.se to unusual frequency responses. It 
is possible that further experimental investigation of 
transducers of this type might yield some units with 
a flat band-pass type of freciuency responses. 


CONFIDENTIAL 
































































































kxpekime;\tal transducers 


187 


Miscellaneous Forms 

There are several miscellaneous forms of lami¬ 
nated, longitudinally oscillating transducers that are 
not includetl in the classifications above. Some of 
the.se are illustrated in Figure 14. These all make use 
of consolidated scroll-type elements made by the 
same process used for commercial Hipersil trans¬ 
former cores. The forms .shown in A and C of Figure 
14 require the use of direct current for magnetic po¬ 
larization but those shown in B and D are polarized 
by means of permanent magnets. 


7.2 EXPERIMENTAL TRANSDUCERS 

7.2.1 Simple Uniform Bars 

Simple uniform bars have not been used as prac¬ 
tical transducers because of the relatively small radi¬ 
ation loading on the availalde face area and because 
of the impossibility of making a continuous active 
face. However, a great many .simjile uniform bars 
have been made and used as half-wave oscillators for 
testing the magnetostrictive properties of .sample ma- 


Table 1. Perfornianco characteri.stics of experimental bookphone elements. 


.Model 

Btaek 

length 

(in.) 

Diaphragm 

Polarization 

Polariz. 

current 

(amp) 

lA 

4..5 

Steel 

DC 

0.0 

■2A 

4..5 

Steel 

Df' 

0.0 

2B 

4.5 

Steel; 





rubber face 

DC 

0.7 

3A 

3.5 

Steel 

DC 

0.8 

4A 

2.5 

Steel 

DC 

1.0 

5B 

4.5 

Steel; no 

Alnico magnet 




flanges; 

at top, plus 




rubber face 

DC 

0.75 

13 A 

4.5 

Polvstvrene 

.Alnico magnets 





top & bottom 

None 

14A 

4.5 

Brass 

Alnico magnet 





at bottom, 





plus DC 

0.7 

17A 

4.0 

Steel 

DC 

2.0 

18A 

4.0 

Cu-plated 

Alnico magnet 




Alnico II 

diaphragm 





plus DC 

0.7 

2nA 

4.0 

Steel; no 





flange.s; 





rubber face 

DC 

1.0 


In all the cases shown in Figure 14 the laminated 
sti-ucture must be cemented, soldered, or brazed to 
the face plates. Also, in all the types shown, the free 
ends of the vibrators con.sist of the rounded portion 
of the wrapped scrolls. The ma.ss and elastic charac¬ 
teristics of the.se rounded ends are difficult to hold 
constant in practice and to analyze theoretically. The 
stiffness of the arches depends to a considerable ex¬ 
tent on the degree of con.solidation. The variations 
in the degree of consolidation that normally occur in 
practice cause the freciuency variations among sup- 
po.sedly identical units to be undesirably large. No 
attempt will be made here to present an analysis of 
the modes and frecpiencies of vibration. 

Several experimental transducers of this type were 
made and tested at HUSL. These will be described 
and di.scus.sed later in this chapter. 


fr 

in 

kc 

Max DC' 
sensitivity 
in db {v/b) 

Mech 

Q 

Efficiency 

Poten¬ 

tial 

From 
air & 
water 

F rom 
acoustic 
measurements 

18.2 

- 79 

12 




19.0 

- 80 

15 

High 


0.10 

18.9 

- 82 

0 

0..55 



23.5 

- 85 

10 

0.43 



32.0 

- 90 

.5.5 

0.13 


0.04 

17.5 

- 85 

11 

0.20 

0.25 

0.275 

18.0 

- 80 

7 

0.065 

0.000 

0.05 

17.0 

- 80 

24 

0.45 

0.43 

0.33 

19.0 

- 90.5 

3 

0.13 

0.15 

0.07 

31.2 






(2nd 






mode?) 

— 80.5 

24 

0.14 


0.10 

19.4 

Not tested 

25 

0.01 

0.42 



terials or the mechanical lo.s.ses in laminated stacks 
consolidated with various cementing materials. 
Freely supported laminated bars have also been used 
as secondary frequency standards becau.se their dif¬ 
ferent modes of viliration give sharji re.sonances, in¬ 
dicated by sharp changes in their impedance. Cor¬ 
rection for the change of frecpiency with temperature 
may be applied in those cases in which extreme ac¬ 
curacy is required. 

7.2.2 Uniform Bars with Pistons 
or Diaphragms 

Bookphones 

Several experimental transducer elements of this 
type were made at HUSL, where they were com- 
monl}'^ referred to as bookphones becau.se of their re- 


CONFIDENTIAL 























LONGITUDINAL.V VIBKATINi; LAMINATED STACKS 


laa 



CONFIDENTIAL 
















































































EXPERIMENTAL TRANSDUCERS 


189 


seml:)lance to books standing on a shelf. An extensive 
series of tests on single elements was made by using 
a special housing in which the elements could be 
changed easily. The housing is shown in section and 
in perspective in Figure 15. The simple bar-shaped 
laminated stacks were made from flat nickel lamina¬ 
tions consolidated with bonding materials such as 
\'inyl.seal resin, phenol-formaldehyde cements, and 
Cycle-Weld cement. The same materials were used 
to bond the laminated stacks to the diaphragm, 
which was made of steel or brass. The moving part 
of each of the diaphragms was in. thick and 1 in. 
square. The entire vibrating element assembly was 
fastened to the housing through the thin compliant 
rim of the diaphragm. The wintlings were supported 
on the laminated stacks by thin pads of Cell-Tite 
neoprene. The lengths of the stacks ranged from 2^^ 
in. to 43 ^ in. The earliest models were polarized with 
direct current while some of the later models were 
polarized by placing Alnico magnets between the two 
stacks at the two ends. 

The results of experiments on cementing the lami¬ 
nated stacks to the diaphragms showed that Bostik 
T46M cement (made by the Boston Blacking and 
C'hemical Company) had the greatest strength. 
Du Pont 4646 and Cycle-Weld C-3 or 55-6 made 
bonds that were strong enough to be cpiite satisfac¬ 
tory. All these joints, when properly made, showed 
tensile strengths of a few thousand pounds per scjuare 
inch. Because the high-frequency alternating mag¬ 
netic flux from the laminated stacks cannot penetrate 
far into the solid diaphragm owing to eddy-current 
shielding, very little is gained by using a cement that 
electrically in.sulates the laminated stacks from the 
diaphragm. Some rather unsucces.sful attempts were 
made to solder the laminated stacks to the dia¬ 
phragms. 

Residts of measurements on some of the experi¬ 
mental elements tested are summarized in Table 1. 
Results of measurements on elements found to be 
defective are not listed. Most of the elements were 
polarized by use of direct current in the windings. 
Some were made with Alnico II magnet inserts be¬ 
tween the two laminated bars, somewhat as illus¬ 
trated in Figure 5. Element 18A was made by using a 
piece of Alnico II magnet material for the diaphragm 
and bonding the laminated bars to it. In no case did 
the magnets give optimum magnetic polarization. 

The best elements were those made with steel dia¬ 
phragms with rubber faces but without flanges. The 
poorest unit (aside from those that were mechan¬ 


ically defective) was the 13A, which was made by 
polymerizing styrene around one end of the assembly, 
as shown in Figure 16. The polystyrene diaphragm 
apparently did not have sufficient stiffne.s.s to tran.s- 
mit the force of the magnetostricti\'e stacks to the 



Figure 16. Laminated double-bar magnetostrictive 
element with Poly.‘^tyrene diaphragm and housing. 

full face area and, in addition, introduced a con¬ 
siderable amount of mechanical damping. This has 
been the usual result when polystyrene and similar 
plastic materials have been used as diajihragms for 
elements of this general type. 

The theoretical frequency for the first mode of vi¬ 
bration of the 43 /^-in. elements as given by equation 
(5) is 18.6 kc. By equation (9) the effective mass is 
211 grams, and by ecpiation (10) the mechanical Q 
should be 26. Differences in the ob.served frecpiencies 


CONFIDENTIAL 

























190 


LONGITUDINALLY VIBRATING LAMINATED STACKS 


of resonance from the values expected theoi'etically 
are ])robably due to slight variations in the lengths of 
the bars and the thicknesses of the diaphragms. In 
.several instances the general shapes of the frecpiency 
responses were rather ragged, due to imperfect joints 
between the laminated bars and the diaphragm and 
to mechanical coupling between the housing and the 
diaphragm. 



Figuke 17. Open-circuit frequency rc.sponse of hook- 
phone, Model 2B Xo. 1. 



Figure 18. Open-circuit frequency response of book- 
jihone, Model 3.\ Xo. 1. 


Some of the observed open-circuit fretiuency re¬ 
sponses are shown in Figures 17 to 21 inclusive. No 
acoustic measurements were made on element 20A. 
However, the impedance diagrams shown in Figures 
22 and 23 show that it was a very efficient element 
and free from spurious re.sonances. 

Only one attempt was made to make a multiele¬ 
ment transducer of the bookphone type. This one was 
known as the line source bookphone. It was made with 
six pairs of laminated bai-s 34 X 1 X 4 in. Each pair 



Figttre 19. Opcn-circuit frequency resjionse of book- 
lihone, Model -l.V Xo. 1. 



Figure 20. Open-circuit frequency respon.se of book¬ 
phone, Model 13.A Xo. 1. 



Figure 21. Open-circuit frequency response of book- 
jihone, Model 17A Xo. 1. 


was cemented together to form an element, with 
Alnico II magnets between the bars at the top and 
bottom ends. The six elements were bonded to a 


CONFIDENTIAL 































































































































EXPERIMENTAL TRANSDUCERS 


191 



0 600 1200 1800 
RESISTANCE IN OHMS 

Figuhe 22. Impedance diagram of hookphone, Model 
20A No. 1 ia air. 


2600 







_140 





















2200 

w 1800 

2 

I 

O 

z 

1400 

z 

< 

O 

< 

UJ 

a 1000 

600 

200 




35 

























3 

0 / 
















2 

5 / 


19 






23 





19.2 




15^ 










1 20 








/ 5 

v'- 

).8 



19.4 




'3 


19.6 

1 







0 200 600 1000 1400 1800 

RESISTANCE IN OHMS 


Figure 23. Impedance diagram of liookphone, Model 
20.\ No. 1 in water. 

brass diapliragm % X I X lOM in. with Bostik 
T46M cement. The length of the diaphragm was di¬ 
vided into six sections by five grooves ]/i in. wide 
and ]4: in. deep to provide some compliance between 
the diaphragm sections to which the elements were 


bonded. The diaphragm was attached to the housing 
by a compliant strip of pc rubber. The housing con¬ 
sisted of a long narrow brass box lined with pressure- 
release material. The entire unit i^roved to be me¬ 
chanically strong and watertight. 

The open-circuit freipiency response of the line 
source bookphone is shown in Figure 24, when the 
polarization due to the Alnico magnets was aug¬ 
mented by 1.4 amperes of d-c ]3olarizing current. The 
primary I'esonance should occur in the region of 20 kc 
and the second resonance in the region of 40 kc. The 
latter appears but the former seems to be smothered 



10 20 30 40 50 60 70 


FREQUENCY IN KC 

Figure 24. Receiving response of line source book- 
phone. 

out by internal damping and spurious mechanical 
resonances of other types. The patterns had high 
minor lobes which indicated considerable variation 
of phase and amijlitude among the elements along 
the diai^hragm strip. Results indicated that refine¬ 
ment in the methods of constructing bookphones is 
recjuired before they can be used in multielement 
transducers where matching of phase and amplitude 
among the elements is of great importance. 

Transducer with T-Shaped Laminations 

A second kind of transducer made at HUSL, in the 
class of laminated bars with diaphragms, was one 
which employed T-shaped laminations of the form 
shown in Figure 25A. The laminations were consoli¬ 
dated to form stacks of the size shown in Figure 25B. 
One multielement transducer was made in which the 
elements were arranged in the pattern shown in Fig¬ 
ure 25C. The crossbar part of the T served as the 
diaphragm and the stem of the T as the longitudinally 
vibrating bar. The faces of the stacks were Cycle- 
Welded to a circular, fiat disk face. The rubber face 


CONFIDENTIAL 




























































































192 


LONGITUDINALLY VIBRATING LAMINATED STACKS 


was stiffened l)y cementing it to a grill of parallel 
bars lying between the rows of stacks without touch¬ 
ing them. The ends of the bars were attached to a 
strong steel ring which surrounded the elements and 
was fastened to the steel face ring which held the 
rubber face. Figure 26 shows the two sectional views 



B 



Figure 2.5. Multielement transducer built from 
T-shaped laminations. 

intlicated by AA and BB in Figure 2.5C. The stacks 
and their windings were supported entirely by the 
thick rubber face. The windings were made up as pre¬ 
formed consolidated coils which fitted clo.sely on the 
stacks but did not touch them. 

The magnets were cemented to a nonmagnetic 
suitiioi'ting plate. The supporting plate was in turn 
supported by the case in such a jtosition that the 
clearance between the magnets and the free ends of 
the stacks was of the order of 0.020 in. Three large 


slablike Alnico magnets were used to jiolarize the 
stacks in pairs, as indicated in Figure 26A. This ar¬ 
rangement made it possilile to polarize the nickel 
stacks to a little below the optimum flux density. The 
high-freciuency alternating flux paths also linked 
pairs of stacks but jumped acro.ss the large air gap 
between pairs because of the shielding effect of eddy 
currents in the solid Alnico magnets. 



A SECTION A-A FROM FIG. 25 C 



Figure 26. Section of the T transcluccr .'<ho\vn in 
Figure 2.5C. 


In this transducer design the cross .section of the 
air path was not much greater than the cro.ss section 
of the nickel stacks, consequently most of the reluc¬ 
tance of the high-frequency flux jiath was due to the 
air path. This decreased the effective reversible per¬ 
meability of the magnetic circuit and so the electro¬ 
mechanical coupling coefficient was much lower than 
that for better designs. 

Open-circuit frequency response of this transducer 
is shown in Figure 27. On the assumption that the 
crossbar of the T would act as a lumjjed mass, the 
frequency of resonance was calculated to be aliout 
6.3 kc. The observed frequency was about .56.3 kc. 
This ^’ariation from the calculated frequency is 
greater than can be accounted for by any error in 
the velocity of sound in the nickel or by transverse 
flexibility of the face bar. The mechanical Q from the 


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EXPERIMENTAL TRANSDUCERS 


I9:i 


observed frequency response was about 32, as com- stack to hold the rubber face against the watertight 
pared to the theoretical value of 70, indicating that metal shell referred to above. 

internal mechanical damping was a little greater than The Alnico V permanent magnet provided a polar- 
water radiation damping. The impedance circle izing flux of approximately 12,000 gau.sses in the legs 
measurements verified this conclusion. The acoustic of the laminated stack. The air gap between the pole 
patterns for this transducer were about as expected 

theoretically, that is, the main lobe was about 17 de- ^ 

... . O O 

grees wide at — G dl) and the first minor lolies were 

about 15 db below the peak. 



FREQUENCY in kc 

Figure 27. Receiving respon.se of the .56-kc T trans¬ 
ducer. 

This type of transducer was abandoned because 
(1) it was difficult to polarize satisfactorily, (2) the 
high-frequency magnetic circuit was inefficient and, 
(3) the mechanical Q was higher than de.sired. 

Bell Telephone Laboratories’ MOX 
Tran.sducer 

A third kind of transducer of this type, called the 
MOX hydrophone, was made and tested by the Bell 
Telephone Laboratories.®- The general shape of the 
laminations used in this hydrophone is shown in Fig¬ 
ure 28A and a diagrammatic representation of the 
essential features of the magnetic circuits and meth¬ 
ods of mechanical mounting are shown in Figure 28B. 
The 0.004-in. 45-Permalloy laminations were an¬ 
nealed in a hydrogen atmosphere at a temperature of 
1050 C. They were consolidated with mineral-filled 
bakelite cement (BC-12996) to form a mechanically 
solid stack. The thickness of the cement between 
laminations was about 0.001 in. 

The rubber face made acoustic contact with the 
water through a thin metal .shell (not shown). The 
laminated stack was mounted in two saddle-like re¬ 
cesses in the main brass supporting ring. A layer of 
jiressure-release rubber was inserted between the 
laminated stack and the brass support ring to isolate 
the vibrating stack from the support ring and to 
transmit mechanical pre.ssure from the laminated 


o o o o 


LAMINATION 
.004” 45 PERMALLOY 



SHOWING the ESSENTIAL FEATURES of Ine MAGNETIC 
CIRCUITS and the MECHANICAL MOUNTING 

Figure 28. MOX liydrophone made by Bell Tele- 

Iilione Laboratories, liic. [BTL]. 

faces of the Alnico magnet was about3^2 *1^- The high- 
frecpiency flux traversed the air gaj) between the two 
legs instead of going through the solid magnet. In 
the actual transducer the plane of the Alnico magnet 
was parallel to that of the face, not in the position 
shown in Figure 28B. 

No data on the open-circuit frequency response 
and patterns of this transducer are available. The 
results given in the BTL report indicated approxi¬ 
mately 50 per cent efficiency at resonance. This trans¬ 
ducer was well designed both magnetically and me¬ 
chanically. Magnetostrictive elements of this kind^ 


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194 


LONGITUDINALLY VTBKATING LAMINATED STACKS 


however, cannot l)e usefully apj)lied in making multi¬ 
element transducers because the i)olarizing magnet 
requires too much interelement space. 

7.2.3 Double or Multiple Bars with 
Symmetrical Closed Ends 

Bell Telephone Laboratories’ CI-100 
Transducers 

Early in the war the Bell Telephone Laboratories 
were given a contract by the Bureau of Ships to de¬ 
velop some impnned magnetostrictive-type trans- 
ilucers which could be substituted for the standard 



Figure 29. L.aininated block element for BTL’s CI- 
100 transducer. 


QC type. Imjirovements in acoustic patterns, effi¬ 
ciency, and u.seful frecpiency band width were desired. 
The first model proposed by BTL for development 
was one made up of an array of laminated stack 
elements, each element consisting of a pair of half¬ 
wave bars with connecting endpieces forming a closed 
magnetic circuit, as shown in Figure 29.® Impedance 
tests on sample elements indicatetl that they would 


satisfy the requirements, ^'arious test models were 
made to determine the best method of mounting the 
laminated stacks to permit one end to radiate into the 
water while the rest of the element was sealed from 
the water. The first method tried was to liond one 
end of the element to a thin (L 32 -in.) steel diaphragm. 
Soldering and cementing with \'arious adhesives were 
tried without much succe.ss. Models were then made 
in which the ends of the elements were imbedded in 
an acoustic rubber face. Results were sufficiently 
sati.sfactory so that a full-sized multiple-element 
transducer was made in this way. Later experiments 
indicated that even better re.sults could be olitained 
by using plastic diaphragms and improved methods 
of con.solidating the laminations into stacks. 

The general a.ssembly drawing of the Cl-lOO tran.s- 
ducer is shown in Figure 30. Forty laminated stack 
elements were cemented to the large, thick rubber 
face. The back ends of the stack elements were heki 
in j)lace by a wire grill with rubber cushions. The 
housing for the laminated stack elements was made 
to fit in a standai’d QC’ projector case. 

The laminations were made of 0.004-in. thick, half- 
hard, A-nickel strip. To flatten the burrs, the indi¬ 
vidual laminations were bumped between hardened 
and polished steel jdates. The outside dimensions of 
the laminations were l}/l in. by “iYi in. and the di¬ 
mensions of the wintlow were Yi in. by 2 in. The 
laminations were coated with a layer of silica gel in¬ 
sulation and con.solidated with BR-0014 bakelite 
resin. The windings were concentrated in the nodal 
region and were bonded firmly to the stack with bake¬ 
lite cement. 

The general wiring diagram is shown in Figure 31. 
The stacks marked “l” each had two coils of 45 
turns, while those marked “2” each had two coils of 
32 turns each. This decrease of turns on the outer 
stacks was used to give some lobe reduction in addi¬ 
tion to that due to the diamond-shaped array. The 
left and right halves of the array were wired sepa¬ 
rately for BDI applications. The stacks were polar¬ 
ized by a component of direct current in the windings. 
This made necessary the u.se of a filter junction box 
with the equipment. A 3-ampere polarizing current 
in each winding was neces.sary to give optimum per¬ 
formance. The complete transducer was jiolarized l)y 
a fi-ampere, 12-volt .source of direct current when 
the two halves were connected in parallel. 

Figure 32 shows a plot of the acoustic pressure pro- 
duccHl on the main axis at a distance of one meter 
per watt of electric input power versus the frequency. 


CONFIDENTIAL 




KXPKKIMENTAI. TRANSDUCERS 


195 



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1% 


U)N(;iTUI)INALLY VIBRATING LAVIINATEI) STACKS 


This is essentially a plot of efficiency against fre- 
cjiiency. Actually impedance varied rapidly with fre¬ 
quency in the region of resonance, so that the open- 
circuit frequency I'csponse cuia-e would l)e much 
sharper than the cur\'e shown in Figure 32. The band 
width over which the efficiency is greater than one- 
half its maximum value is about 4 kc. Other tests 



show('d that the acoustic out])ut was linear up to an 
input of 400 watts. For comparison, the efficiency 
curve for the QCU transducer (one of the best tidi(“- 
and-plate types) and theXl-lOO transducer (a special 
tube-and-plate transducer built for wide band by 
BTL) are also shown in Figure 32. The maximum 
efficiency of the CT-100 transducer occurred at 22 kc 
and had a value of about 40 per cent. 

The acoustic pattern in the horizontal plane, taken 
at 22 kc, is shown in Figure 33. The main lobe was 
about 21 degrees wide at —0 db and 27 degrees wide 
at —10 db. The higher of the first minor lobes was 

— 28 db and the highest of all the minor lobes was 

— 26 db relative to the major lobe. The directivity 
index was about 0.007. The diamond-shai^ed active 
face area and the amplitude shading of the outer 
stacks were ol)\'iously effective in reducing the height 
of the minor lobes. 

This transducer was a definite improvement over 
the standard QC transducer in efficiency, band width, 
acoustic patterns, and j^ower-handling capacity. 
However, the required use of polarizing current made 
it less desirable for practical use than some of the 
permanent-magnet i)olarized tube-and-plate (Re¬ 


types developed at about the same time. Therefore, 
the CT-100 type was not adopted as standard e(piip- 
ment. 

Submarine Signal C’ompany’s 20-kc Fathometer 
Transducer 

The transducer for the 20-kc Fathometer .system, 
manufactured by the Submarine Signal C'ompaiyy, 
consists of a stack of laminations with windings 
around the legs, as shown in Figure 34; the stack is 
houi<ed in a ca,se that is partially filled with castor oil. 
The laminations are punched from jiure nickel strip 
0.010 in. thick and annealed in air at about 1250 F. 
They are stacked without consolidation and held in 
alignment by two lugs projecting from the lamina¬ 
tions at the nodal line. The bottom part of the trans¬ 
ducer case is made of a thin piece of stainless steel, 
which comes in contact with the water on the out¬ 
side and with castor oil on the inside. The laminated 


I 


5 

s 

q: 

£ 



10 15 20 25 50 

FREQUENCY IN kc 


I^'icuRE 32. Transmitting response per watt input of 
irrL^s C’I-100 transducer. 


stack is supported in the case with one of the faces 
near ami parallel to the stainle.s.s-steel bottom. The 
case is filled with enough castor oil to insure that the 
space between the bottom active face of the lami¬ 
nated stack and the stainles.s-steel bottom sheet of 
the ca.se is always full of oil to allow for any reason- 


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EXPERIMENTAL TRANSDUCERS 


197 


able degree of roll or pitch of a ship. The windings 
consist of a few heavy coiuluctors encircling each of 
the two heavy center legs. 


300 * 0 30 * 



Figure 33. Florizontal pattern of BTL’.s CI-100 tran.s- 
ducer at 22 kc. 


During the summer and autumn of 1943, HUSL 
made .several model transducers that used such lami¬ 
nations to test the effect on mechanical damping re¬ 
sulting from consolidation of laminations and from 
immersion of the laminated stacks in oil and in 
water.Each of the experimental laminated stacks 
consisted of 250 laminations {2}/2 bi.). A housing with 
a rubber face was made into which any one of the 
experimental stacks could be placed for testing. Four 
different models were constructed: 

1 . H^alrogen-annealed laminations, unconsoli¬ 
dated, with the entire as.sembly vacuum-filled with 
castor oil. 

2 . Oxide-annealed laminations, unconsolidated, 
with the entire a.ssembly vacuum-filled with castor 
oil. 

3. Oxide-annealed laminations, consolidated with 
Mnylseal resin, with the housing filled with water. 

4. Oxide-annealed laminations, consolidated with 
Vinyl.seal re.sin, with the laminated-stack face Cycle- 
Welded to the rubber face and the stack a.ssemlily 
surrounded by air. 

Electric impedance mea.surements were made with 
these models with and without water-radiation load¬ 
ing. The “cleanne.ss” of the mechanical re.sonance. 


the potential efficiency, and the actual efficiency were 
determined from the impedance vs frequency curves. 
Conclusions drawn from the results of the tests were 
that (1) loose stacking of the laminations encourages 
spurious minor resonances and increa.ses the internal 
mechanical damping; (2) a castor oil film is effective 
in providing electric insulation between bright hydro¬ 
gen-annealed laminations; (3) immersion of a stack 
in castor oil or water causes increa.sed mechanical 
ilamping even though the nonradiating surfaces are 
surrounded by jiressure-release material, such as cor- 
prene; and (4) the best method of mounting lami¬ 
nated-stack transducers is to cement the active face 
of the stack directly to the rubber face and have the 
stack surrounded by air. 



Figure 34. Lamination of Submarine Signal Com¬ 
pany’s 20-kc Fatliometer. 

Ladderphone Transducers 

Early in 1944, some symmetrical multiple-bar, lam¬ 
inated-stack transducers were made at HUSL to de¬ 
termine the effect of mechanical coupling from bar to 
bar due to stiffness of the face sections of the lamina¬ 
tions. ““ The laminations had the general form shown 
in Figure 9B and were made of nickel 0.005 in. thick, 
oxide-annealed at 1000 C. They were bonded to¬ 
gether with C-3 Cycle-Weld resin to form solid stacks 
2 in. high. Each stack had ten bars or legs. One of 
the stacks was left as a solid unit while the other was 
cut into five sections, each containing a jDair of bars. 
Perspective ^'iews of the two laminated stacks are 
shown in Figure 35. Separate windings were placed 
on each pair of bars and a pair of lead wires was 


CONFIDENTIAL 























198 


LONGITUDINALLY VIBRATING LAMINATED STACKS 




P^IGURE 35. Lacldeiphone stacks for measurement on 
mechanical cou[)ling. 



Figure 36. Possible distribution of particle velocity 
along the face of the solid ladderphone stack, center 
section driven. 


brouglit out through tlie cable from each of the wind¬ 
ings. The direction of the windings was such as to 
make the magnetic ])olarities of the bars N-S, S-N, 
N-S, etc., as shown in Figure 35. Each of the trans¬ 
ducer stack assemljlies was Cycle-Welded to a pr 
rubber face and each was housed in a watertight 
rectangular box. Every precaution was taken to 
isolate mechanically the laminated stack structures 
from the housings so that there woidd be no spurious 
coupling effects. 

Electric and acoustic measurements were made to 
estimate the degree of coupling between the sections 


SOLID STACK, IN AIR 
R In OHMS 



Figure 37. Impedance curve.? for solid and .segmented 
ladderphone transducers in air, center section driven. 


within each transducer. The results of the impedance 
vs frequency measurements indicated that when all 
sections were driven together in pha.se both trans¬ 
ducers perfoi’ined alike. However, when only the 
center section was driven, the effects of mechanical 
coupling were very obvious in the unsegmented stack, 
whereas they were absent in the segmented stack. An 
analysis of the acoustic pattern of the unsegmented 
stack transducer showed that if the distribution of 
\’elocity along the face was gamssian when only the 
center section was driven, the .shape of the gau.ssian 
distribution curve would be about as shown in Figure 
36. The effect of the mechanical coupling of the 
center section to the remainder of the unsegmented 
stack was also shown clearly by the .secondary re.so- 
nances which were induced. This effect is shown in 
Figure 37, where the impedance circles of the center 
.sections of the unsegmented and segmented trans¬ 
ducers are compared. 

To investigate further the effect of coupling be- 


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EXPERIMENTAL TRANSDUCERS 


199 



LDPl *1 AA' AXIS 30.4 KC BEAM STEERED TO RIGHT 


330* 0 30* 



LDPl *2 AA' AXIS 30.4 KC BEAM STEERED TO RIGHT 




210- 180* ISO" 

LDPI*2 AA'AXIS 30.4 KC BEAM STEERED TO LEFT 


FifiL’RE 38. p]leeti'ically steered acoustic patterns for solid and .segmented ladderphone transducens. 


tween the segments, an electric phase-tlelay line was 
constructed and connected to the windings of the 
segments so that a phase delay of about 40 degrees 
was introduced in the electric signal between succes¬ 
sive segments. The phase-delay line used was de¬ 
signed to steer the acoustic beam to the left or to the 
right by 10 degrees, depending on which end of the 
line was connected to the source of the signal. Ex¬ 
perimental results are shown in Figure 38. They indi¬ 
cate that the acoustic patterns of each transducer 
can be steered about equally well by the electric 
phase-delay network. The only significant difference 
between the patterns of the two transducers is that 


the null positions caused by cancellation of the sig¬ 
nals from the different sections are more pronounced 
for the segmented stack. This was to be expected 
because each of the small faces of the segments of 
the segmented stacks moved as a unit whereas there 
was probably a smooth change of phase of the 
particle velocity from one end to the other of the face 
of the unsegmented stack. The principal conclusion 
drawn from the results of these tests was that the 
mechanical, magnetic, and electric coupling between 
neighl)oring pairs of legs of the unsegmented type of 
ladderphone is sufficiently low to make its use feasible 
in a multielement sonar transducer. 


CONFIDENTIAL 



























200 


l,ON(;iTlII)IiNALl.Y VIBRATIW; LAMINATED STACKS 


7.2 .1 Double or Multiple Bars with 
Symmetrical Closed Ends and a 
Diaphragm 

Experimental Models Made by I^ell Telephone 
Laboratories 

Several small test models of this type were made 
by BTL.^ Their general characteristics are listed in 
Table 2 and a photograph of Model CT-oO is shown in 


a stiff diaphragm with a i-esulting increase in the face 
mass and the radiation resistance. 

Model IJ-10 is shown in Figure 42. Model IJ-20 
was the same except that the diaphragm was made of 
Liicite instead of polystyrene. The stacks in each of 
these model tran.sducers were built up of nickel lami¬ 
nations 0.002 in. thick. The frecjuency response of 
Model IJ-10, plotted as efficiency (in decibels) vs 
frequency, is shown in Figure 43. The frecpiency re- 
sjionse of Model CI-Go is also shown in the same 


Tabi.e 2. Characteristics of BTL laniiiiatcd block models with diaphragms. 


Mocic4 

Diaphragm 

matc'rial 

Block elements 

F rec]. 
(kc) 

Band 

width 

(kc) 

Efficiency 
(db from 
ideal) 

No. 

Type* 

Material 

Anneal 
(degree.s C) 

CI-.5() 

Rcibbcr 

4 

A 

Nickel 

800 

22.0 

3.0 

- 3.9 

CI-()0 

Lucit(> 

4 

A 

Nickel 

800 

21.0 

5.5 

- 7.9 

CI-(U 

Polvstvronc 

4 

A 

Nickel 

800 

23.0 

3.0 

- 8.4 

CI-6.3 

Lucite 

4 

A 

2V-Permeiulur 

.5.50 

2.5.5 

0.4 

- .5.1 

CI-64 

Bakelite 

4 

A 

Nickel 

800 

21.0 

3.7 

- 3.1 

CT-(i.5 

Lucite 

0 

B 

Nickel 

7.50t 

21.5 

0.5 

- 0.3 

I.I-10 

Polvstvrene 

12 

(' 

Nickel 

800 

35.0 

0.0 

- 8.1 

IJ-20 

Lucite 

12 

(' 

Nickel 

7.50t 

38.0 

9.4 

- 11.0 


*Type A: Lamination^* 1 ^4 X in. with window *4X2 in.; laminations stacked in. high. 

Type B: Laminations X 314 *b. with window *4 X 2 in.; laminations stacked 14 high. 
Type C: Leg section *4 X in.; end section 1 X Vm in. 
t Air anneal: thin cement bonding. 


Figure 39. The four stack elements were cemented to 
a rultber diaphragm 3-2 in- thick and the stacks were 
imbedded in it to a depth of in. Models CT-61 and 
CT-64 were similar to Model CT-GO excejit for the 
diaphragm material, which was jiolystyrene in Model 
C'l-Gl and clear bakelite in Model CT-G4. Model 
CT-G3 was the same as Model CT-GO excejit that the 
blocks were built uji of laminations of 2\'-Permendur 
O.OOG in. thick and annealed at .550 F for ojieration 
on magnetic remanence without polarizing current. 

Model CT-G5, shown in Figure 40, had six nickel 
stack elements, each )/> in. thick, but otherwise the 
dimensions were the same as the stacks used in the 
other models. The laminations were insulated with 
a thin layer of nickel oxide jiroduced by annealing the 
laminations in an air atmosphere at 7.50 F. They 
were consolidated with an unusually thin layer 
(0.0001 in.) of bakelite cement. The spacing between 
the stacks was larger than on the other models. The 
frecpiency response plotted as efficiency (in db) vs 
frecjuency is shown in Figure 41. It has lower peak 
efficiency and lower frequency of resonance but 
greater band width than Model FI-50. This result 
was to be expected if the Lucite diaphragm acted as 


figure for compai’ison. The freciuency response of 
iXIodel IJ-20 was similar to that of Model IJ-10 but 
had a slightly lower peak freciuency. These models 
wei’e designed on the assumption that the dominant 
mode would be that in which the diaphragm would 
be driven as a jiiston, acting as a substantial mass 
load on the lower end of the laminated stacks. This 
mode of vibration is iiresent (21 kc) but the mode 
actually dominant is that at about 34 kc, which is 
neai‘ the natural frecpiency of the free laminated 
stack. 

Some measurements were made of the variation 
of efficiency with input power for the INIodel CT-GO 
test transducer. Results are shown in Figure 44, 
where the sound pressure for five different frecjuencies 
near resonance is plotted against the electric input 
power. In this figure the origin of the decibel ordi¬ 
nate scale is arbitrary. The curves indicate that the 
response is nearly linear for an input of 10 watts or 
less. For greater inputs the respon.se falls off from 
linearity. At a 1.50-watt input the resjwnse is about 
4 db below the value corresjionding to linearity. These 
results indicate that a full-sized Q('-like transducer 
made up of 40 such stacks should be linear up to a 


C'ONFIDENTIAL 


















EXPERIMENTAL TRANSDUCERS 


201 



Figure 39. Working parts of RTF’s Model CI-50 test 
tran.sducer. 



Figure 40. Active part.s of RTF’s Model CI-65 test 
tran.sducer. 



15 17 19 21 23 25 27 29 31 33 35 

FREQUENCY tN KC 


Figure 41. Receiving respon.ses of RTF’s test trans¬ 
ducers, Models CI-.oO and CT-Oo. 



Figure 42. Active parts of RTF’s Model I.I-IO test 
transducer. 


400-\vatt input and should Ijc only 4 db below 
linearity for an input power of 6 kw. Thu.s if the 
CI-100 transducer (.see Section 7.2.3) were driven with 
6-kw input it should produce about 1 kw of acoustic 
power. 

Similar efficiency v.s frequency measurements were 
made on the Model CI-63 transducer (2V-Permendur 


CONFIDENTIAL 











































202 


LONGITUDINALLY VIBRATING LAMINATED STACKS 



FREQUENCY IN KC 


Figure 43. Receiving responses of BTL’s test trans¬ 
ducers, Models I.J-10 and CI-6.5. 



POWER input (WATTS) 

Figure 44. Sound pressure vs electric power input 
for BTL’s Model CI-60 single-stack element. 


stack operating on magnetic remanence). There was 
no apparent demagnetization for power inputs up to 
25 watts per stack element because the response at 
the lower input levels could be repeated after the 
higher level tests were performed. Tests made at in¬ 
put levels greater than 25 watts per stack, using 
polarizing current to maintain the magnetization, in¬ 
dicated a decrea.se in efficiencj- similar to that ob¬ 
served for Model CI-60. 


7.2.5 Double or iMultiple Bars with 
Unsyinmetrical Closed Ends 

Asymmetric Stack Transducers, 9X9 In. 

Two transducers of the asymmetric laminated type 
with active faces 9X9 in. were made at HUSL. The 
laminations used in Model 1 and Model 2 units are 



..1 



LAMINATION FOR MODEL 2 


Figure 45. Lamination.s of Models 1 and 2, 9 x 9-in. 
asymmetrical stack transducers. 


.shown in Figure 45. These transducers were origi¬ 
nally designed for u.se with an early experimental 
sonar that proved unsatisfactory and consequently 
was never adopted or put into .ser\dce use. How¬ 
ever, a laboratory version of the Model 1 trans¬ 
ducer was used as an experimental unit for transducer 
develojmient. One of the goals of this development 
was to produce a magnetostrictive transducer that 
would be an improvement over the conventional 
tube-and-plate type QC’ transducer. The Model 2 
unit was also used as an experimental tran.sducer of 
lower frequency than the Model 1. 

Model 1 Laminations for the Model 1 unit 

were punched from 0.007-in. nickel, annealed in a 
neutral atmosphere at 1000 C, and consolidated with 
General Electric No. 7000 resin to form a stack 8^ 
in. high. Bakelite end plates ^ in. thick and the same 
shape as the laminations were cemented to each end 
of the stack to .serve as winding caps and mounting 
plates. 


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EXPERIMENTAL TRANSDUCERS 


203 


DETAIL' NUMBERS REFER TO TURNS ON CORE; ARROW GIVES DIRECTION OF FLUX IN COREL 

CIRCLES, DOTS AND CROSSES ARE WINDING TERMINALS WITH DIRECTION OF CURRENT 




Figure 46. Details of winding on 9 x 9-in. stack and connectioas in terminal box. 


Tlie legs of the Model 1 transducei- wei-e wound 
with No. 16 stranded wire with Gencaseal insulation. 
It was necessary that this insulation be watertight 
because the entire stack and winding assembly was 
to be submerged directly in sea water. The windings 
were divided primarily into left and right halves for 
BDI applications. Each of the half windings was di¬ 
vided into so-called shaded and filler windings. The 
shaded windings were used for both alternating cur¬ 
rent and direct current, but the filler windings were 
used for direct current only. Each leg of the stack 
was wound with a total of 15 turns of wire. Some of 
the turns belonged to the shaded winding and the 
remainder to the filler winding. The number of turns 
belonging to the shaded winding was greatest for the 
legs at the center of the stack and least for the legs 
near the edges of the stack. This shading of the wind¬ 
ings in which the alternating current passed was to 
i-educe the heights of the minor lobes of the acoustic 


pattern taken in the plane of the laminations. The 
direct current for polarizing the stack passed through 
both the shaded and filler windings so that all legs 
were equally jwlarized. Figure 46A shows a lamination 
on which are indicated the direction of the polarizing 
flux, direction of current flow in the windings, and 
the number of turns on each leg devoted to the 
shaded and filler windings. Figure 46B diagrams the 
layout of terminals in the terminal box. The coils 
shown between pairs of terminals represent the wind¬ 
ings on the laminated stack that are connected to 
those terminals. Each pair of terminals was connected 
to the lead wires from the coils of either the shadetl or 
filler winding on two adjacent pairs of legs of the 
stack. The number of turns of wire between each 
pair of terminals is indicated. 

A rough diagram of the assembled ti-an.sducer is 
shown in Figure 47. A rectangular metal frame sup¬ 
ported the laminated stack and terminal box. The 


CONFIDENTIAL 



















































201 


LONGITUDINALLY VIBRATINi; LAMINATED STACKS 


laminated stack assembly rested on rubber pads and 
the terminal box was fastened in the upper part. The 
side of the terminal box which faced in the same 
direction as the active face of the stack contained 40 
water seals through which the wires of the windings 
entered. The top side of the terminal box contained 
two water seals through which the two main cables 
entered. The side of the terminal box opposite the 
active face was removable .so that the nece.ssary con¬ 
nections could be made within the terminal box after 
all wires and cables were sealed into place. 



Many exiieriments were performed with this trans¬ 
ducer, some of which will be described to illustrate 
several important effects of de.sign and construction 
of laminated stack transducers. 

The effect of polarizing current on the open-circuit 
receiving sen.sitivity is .shown in Figure 48. The mag¬ 
netizing field in the legs was about 5.7 oersteds per 
ampere. Full receiving sen.sitivity was obtained for a 
polarizing current of 4 or more amperes, which coi- 
responds to 15 or more oersteds of magnetizing field. 
The sensitivity at magnetic remanence was about 5 
db below the maximum, but the remanence flux 
density was easily reduced by jarring the stack or by 
driving it lightly with alternating current. This was 
.shown by the fact that at the start of the polarizing 
test the sensitivity was 20 db below maximum al¬ 
though the unit had been polarized during a previous 
test. 



Figure 48. Receiving re.^ponne vs polarizing current, 
Moilel 1, 9 X 9-in. asymmetric stack transducer. 



Figure 49. Impedance in air and in water. Model 1, 
9 X 9-in. asymmetric stack transducer. 


CONFIDENTIAL 
































































































































EXPERIMENTAL TRANSDUCERS 


205 


The first acoustic measurements were made with 
the windings and both front and back faces exposed 
to the water. The impedance curves of Figure 49 re- 
\-eal an important fact: Under these conditions, at 
frequencies away from resonance, the impedances 
(clamped core) when the transducer is in water are 
markedly different from those when the transducer is 
in air. This effect is attributed to the distributed 
capacity of the windings to water, which effects 
partial electric tuning of the circuit and thus renders 
detailed interpretation of impedance data impossible. 



14 le 22 2 6 30 

FREQUENCY IN KC 


Figure 50. Model 1, 9 x 9-in. tran.sducer; open-cir- 
puit receiving response, both faces exposed to the water, 
and no pressure-release material in the winding slots. 



14 18 22 26 30 

FREQUENCY IN KC 

Figure 51. Receiving response with connections as 
shown in Figure 52. 


SHIELD 


-1- 

-HI- 

11 ilil 

- 

! 

1 

' |MM 

BAT 

1 

i 

CHOKE 

onnnnr' 

|OUT 

— axim— 1 —-!- 

— II- 

- ]—>■ 


Si 


PhcuRE 52. Connection for direct current in all wind¬ 
ings and alternating current in shaded windings only. 
Model 1, 9 X 9-in. 





Figure 53. .4. Pattern at resonance, same conditions as in Figure 50 of Model 1, 9 x 9-in. transducer. B. Horizontal 

pattern taken under the conditions of Figure 52. C. Horizontal pattern at frequency of resonance of Model 1, 9 x 9-in. 
asy'mmetric stack with corprene on back face and signal from shaded winding. 


The open-circuit sen.sitivitie.s of the tran.sducer 
with the halves connected in series aiding and with 
windings and both faces exposed to the water are 
shown in Figure 50, where both shaded and filler 
windings were in the a-c and polarizing circuits. In 
Figure 51 the polarizing current passed through all 
the windings, but the a-c signal was picked up on the 
shaded windings only. Figure 52 shows wiring con¬ 


nections for the shaded windings. In the first case, the 
Q was 6.5, only about half what it should have been 
if damping had been due only to radiation resistance 
from the front face. The still lower Q of about 3 in 
the second case indicates an unusually high degree of 
damping due to the “pumping” action in the winding 
slots and the radiation from the back face. 

In Figure 53A and B the radiation patterns at 


CONFIDENTIAL 


























































206 


LON(;nTI)INALLY VIBRATING LAMINATED STACKS 



14 IS 22 26 30 

FREQUENCY 'N KC 

Figure 54. Receiving response of 9 x 9-in. asymmetri¬ 
cal stack after grinding active face. 


Figure 55. Pattern at 23 kc of 9 x 9-in. asymmetrical 
stack after grinding active face. 





Figure 56. A. Pattern at 23 kc of 9 x 9-in. asymmetrical stack with rubber face. B. The same as A but with trans¬ 
ducer completely enclosed. 


peak frequency are .shown for the two conditions just 
mentioned. The effect of a layer of corprene on the 
back face in reducing back radiation is shown in 
Figure 53C. Some reduction of the side lobes pro¬ 
duced by shading is apparent, though not so much 
as would be expected from theory. This and the ab¬ 
sence of widening of the main lobe, which would be 
anticipated on theoretical grounds, could be caused 
bj^ coupling between the center and the edges of the 
stack through the stiffness of the back portion. 

The sharp, exposed edges of the laminations in the 
foregoing experiments facilitated the collection of 
bubbles on the face of the transducer, so that it was 
impo.ssible to determine whether the radiating face 


was uniformly wet. Grinding the transducer face 
smooth proved a partial remedy, and as a result the 
behavior of the transducer was much less erratic and 
more in accord with theory. Figure 54 shows the re¬ 
ceiving respon.se, after grinding, with the two halves 
in parallel and the signal only on shaded windings. 
The increase in sensitivdty is seen by comparison with 
Figure 51. In the latter, the halves were connected 
in series, and when the same jierformance is assumed 
for the two cases the sensitivity in Figure 51 should 
be 6 db higher than in Figure 54. Actually, it was 
onh' 4 db higher, showing a 2-db improvement as a 
result of the grinding. The improvement in pattern 
is shown in Figure 55. 


CONFIDENTIAL 








































EXPERIMENTAL TRANSDUCERS 


207 


Still further improvement in patterns is shown in 
Figure 56. The pattern in A was obtained after a 
3 ^^-in. sheet of rubber was cemented closely to the 
ground face of the transducer but with the windings 
still exposed to the water. The whole tran.sducer was 
then enclosed in a watertight rubber box with the 
edges cemented to the rubber face so that the wind¬ 
ings were no longer in contact with the water. In 
this condition the radiation pattern was as shown in 
Figure 56B, in which reduction of the height of the 
side lobes is to be noted. The peak open-circuit sensi¬ 
tivity was increased, with an increase in Q from 5 to 
8.7. Thus enclosed, the clamped-core impedance 
proved to be the .same in air as in water. 



A SAMPLE OF PRINTER'S INK'IMPRESSION MADE ON NICKEL 
SHEET PREPARATORY TO CUTTING OUT THE LAMINATIONS BY 
ELECTROLYTIC ETCHING. 


B STACK MADE FROM THE ELECTROLYTIC ETCHED LAMIN¬ 
ATIONS. 

Figure .57. Laminated stack used in small experi¬ 
mental 51-kc transducer. 

Experience with this tran.sducer indicated the 
necessity for keeping the windings of laminated 
.stacks free from contact with the water and thus 
influenced the construction of all .subsequent trans¬ 
ducers. 

Model 2 Unit. The laminations of Model 2, 9 X 9- 
in. stack transducer were punched from pure nickel 
stock 0.005 in. thick and 4K in. wide. The face and 
leg structures were the same as in the Model 1 unit, 
so that the solid backing section of Model 2 was 1 in. 
deeper than that of Model 1. The laminations were 
annealed at 1000 C in an atmosphere of hydrogen. 
They were consolidated into a solid block with 


General Electric No. 7000 resin. The stack was 
mounted in a rectangular frame in much the .same 
waj'^ as in Model 1 and the windings were also made 
in the .same way. 

Results of tests were not widely different from 
those on Model 1. They showed that the mechanical 
coupling caused by the transverse stiffness of the 
thick backing section nearly eliminated the effect of 
the shaded windings and also introduced an addi¬ 
tional mode of vibration, which had a frequency near 
that of the principal mode. This complication of the 
modes of vibration was probably enhanced by the 
node l.ving within the solid backing-block section 
which coupled the tran.sver.se motion with the nor¬ 
mal longitudinal motion by the Poisson effect. These 
difficulties indicated that it is poor design practice 
to make either the face plate or the backing plate so 
thick that it includes the node of the principal mode 
of vibration. No further experiments were made with 
the Model 2 tran.sducer. 

51-kc Stack of Electrolytically Cut 
Laminations 

The production of small detailed laminations from 
magnetostrictive sheet material 0.003 in. or le.ss in 
thickness bj^ use of punch-and-die techniques is \"erv 
difficult becau.se punches and dies used on such ma¬ 
terial must fit with unusual precision. An alternative 
to this method is electrolytic etching. Experiments 
in producing thin laminations by this method were 
tried, since it had been used with considerable suc¬ 
cess in cutting templates from steel sheets for use in 
marking out airplane parts. 

An accurate, enlarged drawing of the lamination 
boundaries is made with a wide black line. From the 
drawing a jihotograph is made and reduced to the 
exact size of the finished lamination. This is used in 
etching a copper printing block with the boundary 
lines of the lamination etched in such a way that 
when the block is inked and set in contact with the 
nickel .sheet it makes an ink print of the exact lami¬ 
nation surrounded by a narrow band of unprinted 
area (Figure 57A). While the ink is still damp, pow¬ 
dered dried resin called dragon’s blood is sifted on and 
sticks to the printed portions of the sheet. This is 
then baked to form an impervious, lacquer-like cover¬ 
ing on the inked portions of the sheet. The opposite 
side of the sheet is also coated with a layer of im¬ 
pervious lacquer. The nickel .sheet is then suspended 
in a salt solution and serves as the anode, while a 



CONFIDENTIAL 




















208 


LONGITUDINALLY VIBRATING LAMINATED STACKS 





Figure 58. Receiving response of 51-kc tninsducer 
made from electrolyticallj' etched laminations. 



Figure 59. Pattern at 51-kc of transducer made from 
electrolytically etched laminations. 


submerged lead sheet ser\'es as the cathode. Nascent 
chlorine deposited on the exposed parts of the nickel 
sheet rapidly etches the nickel and in a few minutes 
eats completely through the sheet, so that the newly 
formed lamination is snsj^ended only by the layer of 
lacquer on the back side. The exposed edges of lami¬ 
nations produced in this way are surprisingly square 
and free of burrs. It is technically possible to set up 
an assembly in which this process could be made to 
work continuously on long lengths of thin sheet 
stock. 

Laminations of 0.003-in. nickel were made in this 
way for a small 51-kc stack of the shape and dimen¬ 
sions shown in Figure 57B. The nickel strip was soft- 
annealed before the laminations were etched. The 
lacquer coatings were left on after etching to serve as 
insulating layers, and the laminations were consoli¬ 
dated into a solid stack with Vinylseal resin. The legs 
of the stack were covered with compliant layers of 


air-cell neoprene before the windings were put on. 
The complete stack assembly was mounted in a 
watertight rubber box with the active face of the 
stack C’ycle-Welded to one face of the box and the 
other surfaces lined with air-cell neoprene for pre.s- 
sure release. 

The open-circuit frequency response of the unit 
is shown in Figure 58. The sensitivity was about 
—100 db vs 1 volt per bar and the Q was about 12. 
The acoustic pattern at 51 kc, taken in the plane of 
the laminations, is shown in Figure 59. Efficiency at 
resonance as given by acoustic measurements was 30 
per cent, and as given by impedance circle mea.sure- 
ments, 39 per cent. The performance of this unit was 
good enough that larger multielement transducers 
using similar stacks and mounting were developed. 
These larger transducers were known as SPEP trans¬ 
ducers. They will be ilescribed in some detail later in 
this chapter. 

Two slacks 3.875“ long 
“ " 3.510“ " 



Figitre (iO. Experimental .stepped-frequency trans¬ 
ducer. 


Stepped-Frequency Transducer 

From the earliest days of transducer design at 
HUSL attempts were made to get broad frequency 
response and small rate of change of phase shift with 
frequency by having the vibrating system consist of 
elements which have two or more natural frequencies 
of resonance spaced rather close together. In most 
cases these attempts were unsuccessful because of too 
close mechanical coupling between the various vi¬ 
brating elements or improper coupling with the water. 


CONFIDENTIAL 










































KXPERIMENTAL TRANSDUCERS 


209 




Figure 61. Vector impedance diagram for the stejiped- P^igure 62. Vector impedance diagram for the stepped- 

frequency transducer in air. frequency transducer in water. 



I'lGURE 63. Receiving resjionsc of the stepjicd-frequency transducer. 


Ill an attempt to make a tfansdiieer with lii’oad 
frecjiiency re.sponse, an experimental unit containing 
elements having three different natui’al li'equencies, 
all linked by the same winding, was made and tested 
at HUSL. The essential parts of the transducer are 
shown in Figure 60. The assembly was mounted in a 
watertight metal box with the pc rubber face in con¬ 
tact with the water. The indii idual stack elements 
each had faces that were a small fraction of a wa\'e 
length wide (in water) and were mechanically i.so- 
lated from one another by thin layers of air-cell neo¬ 
prene. 


The vector impedance diagram for the assembled 
transducer in air (unloaded) is shown in Figure 61, 
and that for the transducer in water is shown in 
Figure 62. The motional impedance circles corre¬ 
sponding to the three different frecpiencies of reso¬ 
nance stand out clearly in both the air and water 
measurements. The open-circuit frecjuency respon.se 
of the unit is shown in Figure 63. The three reso¬ 
nances at 21.5 kc, 23 kc, and 25 kc are pronounced 
and have the general effect of holding the response 
to a unifoi'in value over the frecpiency i-ange from 20 
kc to 27 kc. 


CONFIDENTIAL 


































210 


LONGITUDINALLY VIBRATING LAMINATED STACKS 


hile this transducer was being given acoustic 
tests in water, the phase difference between the elec¬ 
tric signal generated in the windings and the sound 
signal in water was measured. The results are given 
in Figure 64. In the general design of the transducer, 
the mechanical phase angle (relative to the sound 
signal) of one of the elements was e.xpected to be 
nearly canceled by that of another of the elements. 



Figure 64. Pha.-^e difference between electric .signal 
and acoustic signal as a function of frequency for the 
stepped-frequency transducer. 


since one would be above its frequency of resonance 
while the other would be below; therefore, the me¬ 
chanical phase angles of the two sections would be 
about equal in magnitude but opposite in direction. 
Figure 64 shows that this effect was nearly attained. 
It appears that if the stack .sections that re.sonated 
at 23 kc and 25 kc had been made a little thicker in 
comparison with the 21.5 kc sections the desired 
phase behavior would have been more nearly ob¬ 
tained. 

The acoustic mea.surements indicated that the effi¬ 
ciencies at 21.5 kc, 23 kc, and 25 kc were about 9 per 
cent, 6 per cent, and 5 per cent, respectively. These 
efficiencies were approximately one-third of those for 
similar transducers made of single-frequency stacks. 
This lowered efficiency was primarily due to the fact 
that only about one-third of the total stack con¬ 
tributed to the generated signal at any one frequency, 
while the whole structure contributed to the core 
losses. This resvdt is in agreement with the general 


principle that anj" broadening of the band width of 
frequency response can be obtained only at the ex¬ 
pense of the efficiency. Thus in practical applications 
the best compromise between the band width of re¬ 
sponse and the efficiency must be chosen. 

Direct-Current Polarized SPEP Transducer'-® 
Following the .succe.ss of the small experimental 
51-kc laminated stack transducer de.scribed above, 
a multielement, flat-faced tran.sducer containing 32 
small laminated .stacks designed for about 60 kc 
was made. The laminations had the shape and di- 
men.sions shown in Figure 65A and were punched out 
of 0.005-in. nickel strip. These laminations were 
cleaned, annealed in air at 1000 C, and consolidated 
with C'-3Cycle-Weld resin to form stacks ^{5 in. high. 



Figure 6.5. Nickel laminations and stacks of the 60-kc, 
d-c polarized, .SPFiP transducer. 


as shown in Figure 65B. Windings were placed around 
each of the two leg.s with thin layers of air-cell neo¬ 
prene to isolate mechanically the winding from the 
laminated stack. The direction of the windings was 
such as to make the magnetic flux go up one leg and 
down the other. In this way the entire magnetic cir¬ 
cuit for both the polarizing flux and the high-fre- 


COXFIDENTIAL 

















































EXPERIMENTAL TRANSDUCERS 


211 


cjiiency flux lay entirely within the nickel lamina¬ 
tions; consequently, the electromechanical coupling 
coefficient approached the maximum possible for 
nickel. 

The active faces of the laminated stacks were 
Cycle-Welded to a flat disk-shaped pc rubber face 
1 in. thick, as indicated in Figure 66. The array of 
stacks was as shown in Figure 67. The planes of the 
laminations in neighboring stacks were placed at right 
angles to each other to minimize magnetic coupling 
between stacks and to make the inactive space be¬ 
tween stacks ecjual on all sides of the stacks. The 




Figure 67. Stack arrangement viewed from the rear 
in SPEP Model No. 1 transducer. S figure.s are the 
turns of shaded winding (a-c and d-c). F figures give 
filler w'inding turns (d-c only). 


A. sectional view 
OF SPEP MODEL I 
TRANSDUCER. 

0 PERSPECTIVE 
VIEW OF INDIVID¬ 
UAL SPEP STACK. 

STACK ELEMENT 

Figure 66 . Section of Model 1 d-c polarized 60-kc 
SPEP traasducer. 

windings were di\'ided into four quadrants corre¬ 
sponding to the geometrical quadrants to the trans¬ 
ducer. To minimize the heights of the minor lobes of 
the transducer’s acoustic pattern, the number of 
turns of the windings devoted to the high-frequency 
current in the outer stacks was fewer than for the 
center stacks. The.se windings were called the shaded 
windings. However, in order to produce equal polar¬ 
ization of all the stacks, an additional filler winding 
was placed on each stack to make the total number 
of turns the .same. The polarizing current was allowed 
to flow in both the shaded and the filler windings. 
On each stack the total turns devoted to the shaded 
and filler windings are indicated in Figure 67 by the 
numbers following the S’s and F’s marked on each 
stack. Three wires were brought out from each 
quadrant, the +wire of the S winding, the common 

— of the S winding and + of the F winding, and the 

— of the F winding. 


96 ANNEALED NICKEL 
LAMINATIONS .005" THICK CONSOL¬ 
IDATED WITH C-3 CYCLE-WELD. 


TOTAL OF 50 
TURNS, MADE 
UP OF SHADED 
AND FILLER 
WINDING. 



2 

*85 


IaJ 

z 

> -90 
o 

-95 

O 

> 

- -100 
i/) 

> 

^ -105 

z 

- -no 
> 

> -115 

K 

(ft 

5 -120 
w 3 




































0 40 5 0 60 70 8 


FREQUENCY IN KC 

Figure 68 . Receiving response of the Model 1, d-c 
polarized, 60-kc SPEP transducer, all quadrants in 
parallel. 

The rubber face .shown in Figure 66 was Cycle- 
Welded into the steel face ring before the laminated 
stacks were Cycle-Welded to the rubber face. Both 
these Cycle-Welding operations required the use of 
special jigs to hold the various parts in place during 
the curing process. 

The back part of the hydrophone ca.se was con¬ 
structed so that it made a watertight seal against the 
steel face ring and also supported the back ends of the 


CONFIDENTIAL 















































































































































































212 


LONGITUDINALLY VIBRATING LAMINATED STACKS 



Figuhe fitt. Pattern at 08.4 kc of Model 1, d-c polar¬ 
ized, tiO-kc iSPEP transducer, signal from shaded 
windings, axis of rotation parallel to one side of the 
square array. 


3S0" 0 * 30* 



input to shaded windings, axis of rotation parallel to 
one side of square array. 


330* 0* 30" 



Figure 70. Pattern at .'iS.I kc of Model 1, d-c polar¬ 
ized, 60-kc SPEP transducer, signal from full windings, 
axis of rotation parallel to one side of the square array. 


laminated .stacks through a thin layer of air-cell neo¬ 
prene. The entire transducer was made to fit in a re- 
ce.ss in a special hemispherical baffle of approximately 
9-in. radius. 

The electric and acoustic performance of this trans¬ 
ducer was unusually good. The open-circuit fre- 
tpiency response for all four (piadrants connected in 
parallel is shown in Figure 68. The Q was about 9 and 
the efficiency about 25 jtcr cent. Figure 69 shows the 



Figure 72. Itcnr view of stuck :is.seml)ly in .'SPI'IP 
Model No. 2. 


Itattern of the transducer as a receiver at 58.4 kc 
taken about an axis jjarallel to one side of the scpiare 
array when the signal was taken from the .shaded 
windings. When the axis of rotation was parallel to a 
diagonal of the scpiare array, the side lobes were even 
lower than those shown in Figure (59. Figure 70 .show.s 
the pattern of the unit as a receiver at 58.4 kc taken 


CONFIDENTIAL 
























































EXPERIMENTAL TRANSDUCERS 


about an axis parallel to a side of the square array 
when the signal was taken from the full windings. 
1 his .shows that the effect on the height of the minor 
lobes due to shading of the windings on the stacks is 
pronounced, as predicted l)y theory. Figure 71 shows 
the pattern of the unit as a projector at 58.4 kc when 
the input power on the shaded windings was 40 watts 
and the axis of rotation was parallel to one side of the 
square array. The measured efficiency of the unit 
under these conditions was about 30 per cent. 

As soon as it became evident that the SPEP trans- 


21.J 


made with special steel cases, special molded rubber 
faces with spherical curvature, and special aluminum 
grillwork to help support the back ends of the stacks. 
Figure 72 shows the array of stacks Cycle-Welded to 
the rubber face. The rubber faces for the.se units were 
molded from natural rubber compounds. The finished 
moldings had durometer hardnesses of about 35 to 
45 and were as free as possible from poro.sity. 

Model 3 was the same as Model 2 excejff that the 
aluminum grillwork used to support the back ends of 
the stacks in Model 2 was replaced by snugly fitting 



FuiURE 7.3. .Section of SPEP Model No. 6 (PM-iK>lari5!ed). 


ducer would satisfy the various acoustic and electric 
specifications retjuired, design work for a more rugged 
and better-engineered unit was begun. Six different 
tyites. Models 1 through G, were made. Models 1 
through 5 used laminated stacks polarized with di¬ 
rect current, while Model 6 used stacks polarized with 
sintered-oxide permanent magnets. 

The two Model 1 units were similar to the origi¬ 
nal SPEP de.scribed above. 

44ie nine Model 2 units constructed and tested were 


pads of corprene. This made the array of stacks more 
resilient, so that the units could withstand severe me¬ 
chanical shocks better than the Model 2 units. 

In Models 4 and 5 attempts were made to construct 
I’ubber faces that had thin metal reinforcement plates 
either cemented to the outside of the face or molded 
inside the rubber. On Model 4 the reinforcement con¬ 
sisted of a 0.010 in. thick, stainless-steel spinning, with 
the same radius of curvature as the outside face of 
the rubl)ei’, which was Cycle-Welded to the fi-ont 


CONFIDENTIAL 




















































































211 


LON(;rn:i)INALLV VIBRATINi; LAMINATED STACKS 



A SPEP STACK WITH MAGNET SLOT 



B THREE SIZES OF MAGNETS USED IN 
EARLY TEST STACKS 

Figure 74. SPFT stacks modified for iiolarizatioii tiy 
sintercd-oxidc magnets. 


was molded in the rubber face when it was made. This 
unit proved to be entirely unsatisfactory because of 
poor acoustic transmission through porous places in 
the rubber face next to the metal, where gas bubbles 
were trapped. It was eventually found that rubber 
faces with a durometer hardness of about 70 and 
without any metal reinforcement were more .satis¬ 
factory. 

Permanent Magnet (PM) Polarized SPEP 
Tr.vnsducer 

The Motlel 6 SPEP transducers were es.sentially 
the .same as Model 3 except that the laminated stacks 
were polarized with sintered-oxide permanent mag¬ 
nets. A cross section of this model is shown in figure 
73. Twenty-.seven units of the Model 6 SPEP trans¬ 
ducers were made and tested. From the point of view 
of transducer design and development the most im¬ 
portant feature of this model was the PM polariza¬ 
tion. 

The first tests on the use of sintered oxide as a per¬ 
manent magnet material for jiolarizing laminated 
transducer stacks were made on SPEP stacks of the 


T.\bi.e 3. Rcsult.s of imiiedaiice measurements for permanent magnet polarized stacks SPEP-PMI No. 1, SPEP- 
PMI No. 2, SPEP-PMI No. 3, and a standard direct-current polarized stack. 



No. 1, 
full magnet, 

0 pol cur 

No. 2, * 

magnet 

No. 3, ^ 

magnet 

DC pol SPEP 
stack, 1.25 amp 
pol cur element 
No. 2 


0 pol cur 

1.5 amp 
pol cur 

0 pol cur 

2.0 amp 
pol cur 

7j clamped @/r 

2.2 -t- jl9.8 

3.0 4- j23.6 

1.71 -h J16.25 

5.5 -|-j31.4 

2.45 -f- j\9.7 

13.6 +jol 

14.1 -L .53@60kc 

Du 

10.7 

7.8 

3.6 

11.7 

4.4 

58 

fr 

.50.96 

60.75 

61.2 

.59.30 

61..50 

57.43 

Za. @fr 

12.4 -1- jl6.6 

10 +j2Q 

5.0-f-jl5 

17+j29.5 

.5.1 -kil7.5 

63 -F >20.5 

Qa 

34 

1.5.6 

22.6 

16 

16 

37 

k = VDa/QaX 

0.127 

0.146 

0.099 

0.1.52 

0.117 

0.176 

2r.„ 

17..5° 

27° 

20..5° 

9.0° 

30..5° 

31° 

'^max/'^min 

1.62.5 

1.38 

1.19 

1.34 

1.18 

3.40 

Pot eff 

0.412 

0..327 

0.277 

0.275 

0.258 

0.445 

■Area of magnet 
.Area of one leg 

6.06 

4.55 

4..55 

3.03 

3.03 

No magnet 

Quality of stack 

Good 

Mediocre 

Mediocre 

Mediocre 

Mediocre 

Good 


surface of the rubber face. This unit was unsuccessful 
because perfect bonding was not obtained between 
the metal and rubber. The frequency respon.se and 
the acoustic patterns were therefore unsatisfactory. 

In Model 5, the reinforcement consisted of a 0.01.5 
in. thick, dish-shaped piece of stainless steel which 


form shown in Figure 65B, which was modified by 
cutting a iri the backing portion to make 

stacks of the form shown in Figure 74A. The first 
three experimental test stacks had three different 
.sizes of magnets, as shown in Figure 74B. Results of 
impedance tests on these three stacks, as compared 


CONFIDENTIAL 























































EXPERIMENTAL TRANSDUCERS 


215 


to a conventional d-c polarized stack, are given in 
Table 3. All the stacks had a standard 50-turn wind¬ 
ing. Impedance measurements were also taken on 
PM stacks No. 2 and No. 3 when the polai'ization was 
increased by some direct current in the windings. 

Comparison of the electromechanical coupling co¬ 
efficients k, listed in Table 3, indicates that stacks 
1 and 2 were somewhat overpolarized by the mag¬ 
nets, since the highest k was found for stack 3 with¬ 
out polarizing current. The gap in the magnetic path 
in the PM polarized stacks decreased the effective 
reversible permeability of the stacks, with a conse- 
cpient decrease in k as compared with the d-c jiolar- 
ized stack that had a complete magnetic circuit. 



CO 


z 

Z) 

(O 

o 

o 

z 


cc 


Figure 75. Effective reversilile iienneafiility and 
reluctance \'.s flux density in the legs of a PM-polari/ed 
SPEP stack. 


SO near the calculated curve indicates the correctness 
of the theory. The po.sitions of the observed values 
along the line are a good indication of the degree of 
polarization of the stacks. These results indicated 
that the three-quarter sized magnet would give the 
proper degree of polarization for maximum efficiency. 



Figure 70. C'alculated and observed clamped core 
impedance of PM-jiolarized SPEP stacks at 60 kc for 
various degrees of polarization (50-turn winding'). 


The clamped-core impedance of the stacks was 
considered to be a better criterion of the actual de¬ 
gree of magnetic polarization of the stacks than the 
electromechanical coupling coefficients. The effective 
reversible permeability of the PM polarized stacks was 
calculated from the geometry of the stacks and the 
results of static magnetic measurements on samples 
of similar nickel. The reluctance and effective per¬ 
meability are plotted against the flux density in the 
nickel legs of the stacks in Figure 75. At high flux 
densities the permeability decreases rapidly, due to 
saturation of the nickel. Figure 76 shows the clamped- 
core impedance diagrams for PM-polarized SPEP 
stacks which were calculated from the Mr’s given in 
Figure 75. Observed values of the clamped-core im¬ 
pedances for the various PM stacks are indicated on 
the same graph. The fact that the observed values lie 


However, these magnets were magnetized to their 
highest value and it was pointed out that the final 
transducer would be more stable if the full-sized 
magnets were used and partially depolarized while in 
place in the nickel stack. Consequently, all the sub¬ 
sequent PM polarized SPEP stacks were equipped 
with magnets which filled the entire magnet slot. 

Figure 77 shows the clamped-core impedance dia¬ 
gram for d-c polarized SPEP stacks made of 0.005-in. 
oxide-annealed nickel where the flux density is the 
parameter. The observed clamped-core impedance 
for a stack polarized with a 1.2-ampere polarizing 
current is shown on the same graph. The position of 
the observed point indicates that the stack was 
underpolarized (B = 3,200) and that 2.4 amperes 
would be required to polarize it for optimum effi¬ 
ciency. The most outstanding difference between the 


CONFIDENTIAL 












































216 


LONGITUDINALLY VIBRATING LAMINATED STACKS 


impedances of the d-e and PM polarized stacks is 
that the magnitude of impedance for the d-c polarized 
stacks in the region of B = 4,000 is roughly twice 
that of the PM polarized ones. This means that for 
the region oi B = 4,000 the introduction of the mag¬ 
net slot in the stack decreases the effective reversible 
permeability to about one-half the value for the un¬ 
slotted stacks. 


radiation, then the efficiency is given by the ratio of 
the water impedance circle diameter divided by the 
resistance at resonance. The efficiencies for the two 
kinds of stacks are plotted again.st the polarizing 
flux density in Figure 80. 

The PM polai'ized SPKP stack which contained 
the full-sized magnet was inserted in a watertight 
rubber housing so that electric and acoustic tests 



Figure 77. Calculated clam|)ed-core impedance of a 

d-c polarized SPEP stack with 50-tuni winding. 

Becau.se the electromechanical coupling coefficient 
and the eddy-current factor \-ary with the degree of 
polarization, the size of the motional impedance cir¬ 
cle on the vector impedance diagram is zero for zero 
polarization, increases to a maximum size for the 
polarization which gives maximum coupling, then 
decrea.ses in size for greater polarization. Figures 78 
and 79 .show in graphical form the loci of the ends of 
the resonance diameters of the motional impedance 
circles when the}^ are added vectorially to the cor¬ 
responding points (same polarization) on the 
clamped-core impedance lines. Figure 78 is for the 
PM polarized stacks and Figure 79 for the direct-cur- 
rent polarized stack. If it is assumed that all the 
mechanical power lo.ss in the stacks is due to acoustic 


cn 

5 

X 

o 

X 



R IN OHMS 


Figure 78. Total impedance at resonance of PM- 
polarized SPEP stack, oO-turn coil, in water for various 
degrees of jiolarization. 


cotdd be made in water as well as in air. The tests 
showed it to have a Q of 37 in air and a Q of 7.5 in 
water. The efficiency was 0.43, as determined from 
the diameters of the air and water motional imped¬ 
ance circles and the total resistance at resonance in 
water. Considering that some of the mechanical 
power loss was in the stack itself, this result was in 
good agreement with the value of 0.63 indicated in 
Figure 80. 

The use of PM polarized stacks in the SPEP tran.s- 
ducer simplified its construction to a considerable ex¬ 
tent because only a single winding was needed on 
each stack and only two lead wires from each quad- 


COXFIDEXTIAL 


















































KXPEKIMENTAL TRANSDUCERS 


217 



0 10 20 30 40 50 


R IN Ohms 

Figure 79. Total impedance at resonance in water for 
various degrees of polarization of d-c jiolarized SPEP 
stack, oO-turn coil. 



Figure 80. Kfficiencj' of SPEP stacks as a function of 
the degree of polarization. 


rant. T 3 ^pical vector impedance plots in air and in 
water for a complete Model 6 SPEP transducer are 
shown in Figures 81 and 82. These impedance data 
show the mechanical Q of the unit to be about 12.5 
when it is loaded b\" water radiation and the effi¬ 
ciency at resonance to be about 54 per cent. Both 
these values are nearlj^ up to the theoretical values 



Figure 81. Vector impedance curve for SPEP No. 6 
in air. 


for a perfect transducer of this type. Figure 83 shows 
the acoustic pattern of a good SPEP 6 transducer, 
taken at 60 kc about an axis parallel to one of the 
diagonals of the square arra.v of stacks. The response 
in the directions for which the curve is not given was 
below the —40 db level. This pattern approximates 
veiy closety the gaussian pattern (without side lobes) 
which was originally desired for this transducer. 

To investigate the performance of the SPEP trans¬ 
ducer at high electric input power levels, measure¬ 
ments were made on some single PM polarized SPEP 
stacks mounted in rubber housings.®^'Steadystate 
measurements at verv high levels were impractical 
because of damage to the stack from overheating. The 
measurements were made with power pulses approxi¬ 
mating 0.015 second in length, 2)4 pulses per second. 
Driving currents up to 3.84 rms amperes were used, 
corresponding to input powers up to 150 watts. The 
wave form of the acoustic output remained sinusoidal 
for all the input powers used. This was attributed to 
the mechanical Q of the s\'stem being high enough to 
give a mechanical filter effect. The acoustic output 
power was nearh" linear up to 60 watts of electric 
input but dropped below linearit\' for higher input 
powers. No cavitation effects were observed at the 
active face of the stack during the short pulses, de¬ 
spite the fact that the acoustic power flux was as 
great as 15 watts per sci cm, which corresponds to 
about seven atmospheres of acoustic pressure. The 
maximum possible acoustic power output is limited 
by magnetic saturation and is about 30 watts per 


CONFIDENTIAL 
































































































218 


L(>N(;iTUI)INALLY VIBRATING LAMINATED STACKS 



Figure 82. Vector imiiedance curve for SPEP Xo. (i 
in water. 


330* O* 30" 



Figure 83. Acoustic pattern at 60-kc of an SPEP 6 
transducer taken about an axLs parallel to a diagonal 
of the square array of stacks. 



Figure 84. I>ayout of SPEP stacks in sword-arm 
depth-angle transducer showing the total number of 
turns of winding on each stack. 



Figure So. Completed (iO-ke sword-arm depth-angle 
transducer. 


CONFIDENTIAL 





















































EX P KKIM ENTAL TR A> SDECER S 


219 


WATERSEAL 
GLAND 


BRONZE CASTING 


RUBBER 


STAINLESS 
FRAME 


STAINLESS-STEEL 
SHELL 



FREE-FLOODING CHAMBERS 


PERMANENT MAGNET 
POLARIZED, LAMINATED 
NICKEL STACKS 

Figure 86. Section in place perjiendicular to long axi.s midway along the length of a 60-kc sword-arm depth-angle 
transducer. 



Figure 87. Open-circuit frequency response for series 
and parallel connections of 60-kc sword-arm depth- 
angle transducer. 


stack. For a whole SPEP transducer thi.s corresponds 
to a total input power of about 1,500 watts to pro¬ 
duce about 250 watts of acoustic output. This has 
been verified experimentally in high-power pulsing 
tests on full-sized SPEP transducers. 

60-kc Sword-Arm Depth-Angle Transducer 
During the first half of 1944, a special sword-arm 
depth-angle transducer was de.signed and made at 
HUSL to be used as an echo-ranging tran.sducer to 
determine the depth angle of deep underwater tar¬ 
gets. The active part of the transducer consisted of a 
long, narrow array of thirty-two 60-kc PM polarized 


<f JO* 



Figure 88. Pattern in horizontal plane at 61.2 kc, 
parallel-aiding connection of 60-kc sword-arm depth- 
angle tran.sducer. 


SPEP stacks arranged as shown in Figure 84. The 
long axis of the tran.sducer was in the vertical direc¬ 
tion so that the acoustic pattern in the vertical plane 
was sharp while that in the horizontal plane was 
broad. A photograph of the completed transducer is 
shown in Figure 85. The molded rubber face to which 
the laminated stacks were Cycle-Welded appears on 
the lower front edge. The top section of the structure 
was a stainles.s-steel sleeve u.sed in attaching the 
transducer to the streamlined strut mounting. A sec- 


CONFIDENTIAL 































































220 


L()N(;iTl'DINALLY VIBRATING LAMINATED STACKS 



240" 210° ISO” 150' 120° 


Figuhe 89. Pattern in vertical plane at 01.2 kc, 
parallel-aiding connection of (iO-kc sword-arm depth- 
angle transducer. 



10 20 30 40 50 60 

FREQUENCY IN KC 


Figuke 90. Receiving response of Models OA, 7.\, 
lOA, and lOH hairpin transducer units. 


tion of the transducer taken at the center of tlie 
length of the active ])ortion is shown in Figure*86. 

All the stacks in both upper and lower halves were 
connected in series aiding. Separate lead wires were 
brought out through the cable from each of the halves 
so that the transducer could give BDI operation in 
the vertical plane. The number of turns on the stacks 
was decreased parabolically from 50 at the center 
to 14 at the ends in order to give minor lobe sup¬ 
pression. 

Results of impedance measurements on the trans- 
ducei’ in air and water are listed in Table 4. These 


show that the bottom half was not so good as the top 
half. The imi)edances of the two halves, separately or 
in parallel, were consistent, but the impedance of the 
two halves in series differed widely from the ex¬ 
pected value of four times that of the two halves in 
l^arallel. The variation was caused by electric tuning 
due to distributed capacity in the winrlings and the 
cable. 


T.\bi,e 4. Analysis of impedance measurement.s on 
the ()0 kc sword-arm depth-angle transducer. 



Top half 
alone 

Bottom 
half alone 

Two halves 
parallel 

Two halves 
ill series 

Jr 

.59.98 

t)0.20 

00.00 

00.20 

<)a 

35 

35 

35 

21 

y.c 

87 + jdol 

110 -h j350 

43 -h jl71 

lOSO -1- j480 

Da 

245 

174 

114 

020 

k 

0.14 

0.12 

0.14 

0.15 

Fot (>ff 

0.;54 

0.25 

0.34 

0.20 

/r{ water) 

59.7 

59.9 

59.9 

01.2 

Vir 

11.0 

10.0 

10.3 

11.1 

y.e 

95 + j342 

94 + j340 

40 -h jl71 

920 - jl25 

y at Jr 

ISO -h j297 

172 -I- j300 

87 + jl49 

73 -h jO 

1)\V 

97 

75 

47 

230 

k 

O.lti 

0.10 

0.10 

0.15 

Eff 

0.42 

0.25 

0.32 

0.20 



Figure 91. Ojien-circuit frequency res|)onse of Models 
llA and IIH hairpin transducer units. 


The open-circuit freciuency responses of the unit 
for the parallel and series connections are shown in 
Figure 87. The difference between the resjionses for 
the series and parallel connections should be ex¬ 
actly 6 db, but the actual difference is more than 
this, due to the electric tuning effect for the series 
connection. 


CONFIDENTIAL 













































EXPERIMENTAL TRANSDUCERS 


221 


The pattern in the horizontal plane at 61.2 kc is 
shown in Figure 88 and for the vertical plane in Fig¬ 
ure 89. The heights of the side lobes in the horizontal 
plane pattern were approximately as expected, while 
those in the vertical plane pattern were considerably 
higher than they should have been for the degree of 
shading used. The only explanation that has been 



0 100 200 


RESISTANCE IN OHMS 

Figure 92. Vector impedance locus jilot for liairpin 
transducer Model lOB. 

given for this deviation from theory is that there may 
have been some phase variation along the length of 
the array of stacks, due to distributed capacity in the 
windings. 

Only one unit of this type was made becau.se a 
crystal transducer developed by BTL to serve the 
same purpose was demonstrated and accepted before 
this magnetostrictive unit was completed. 

Sonar Transducer Elements 

The elements of most of the magnetostrictive sonar 
transducers made at HUSL consisted of stacks of 
laminations of the form .shown in Figure llC and D. 
The models actually made and tested were HP-1, 
HP-2, HP-3, HP-5, and HP-8. 


7.2.6 Miscellaneous Forms 

Some of the miscellaneous forms of laminated lon¬ 
gitudinal vibrators have been shown above in Figure 
14 and discussed generally in Section 12. All four of 
the forms illustrated in Figure 14 have been investi¬ 
gated experimentally to some extent at HUSL. None 
of them showed any promise of giving stable repro¬ 
ducible frequencies of re.sonance, high efficiency, or 
uniform acoustic patterns. As pointed out in Section 
12, one cause of trouble is the variation in the exact 
shape and degree of consolidation of the arched por¬ 
tion of the laminated structure. A .second is the 



RESISTANCE IN OHMS 


Figure 93. Vector impedance locus plot for hairpin 
transducer Model IIB. 

mechanical joint between the laminated structure 
and the face plate, and a third is the relatively poor 
high-frequency magnetic circuit between the free 
ends of the laminated structures of the types shown 
in Figure 14A, B, and D. In these cases the high-fre¬ 
quency flux cannot pass freely between the two arms 
of the laminated structure because of eddy-current 
.shielding in the inner laminations. The type .shown 
in Figure 14C does not suffer from this difficulty. 

Eight experimental models of the forms shown in 
Figure 14A and B were constructed and tested. The 
hairpin-shaped laminations were made from oxide- 
annealed nickel 0.005 in. thick by 1 in. wide by the 
Westinghouse Electric Company, using the .same 


CONFIDENTIAL 





































222 


LONGITUDINALLY VIBRATING LAMINATED STACKS 


process as for commercial Hipersil transformer cores. 
The thickness of the stack of laminations was ]/^ in. 
and the distance from the flat open end to the outside 
of the arch end was 2]/2 in. The.se laminated struc¬ 
tures were cemented to diaphragm pieces 1 X 1 X 
in. thick and were mounted in the housing used for 
testing the bookphone transducer models (Figures 15 
and 16). 


principal one. Some of the units also .showed con¬ 
siderable response at the .second principal mode of vi¬ 
bration in the region of 45 kc. The vector impedance 
locus plots for Model lOB, one of the poorest of the 
units, are shown in Figure 92, and for comparison the 
.same type of plots are shown in Figure 93 for Model 
IIB, one of the best. 

On the whole, the performance of the hairpin tyj)e 


Table 5. Performance characteristics of experimental “hairpin” laminated stacks. 










Efficiency 









Poten- 

From air 

P'rom 


Stack 



Polarizing 


Max OC 


tial 

and water 

acoustic 


length 



current 

fr 

sensitivity 

Mech 

(per 

impedance 

meas. 

Model 

(inches) 

Diaphragm 

Polarization 

(amp) 

(kc) 

db (b/v) 

(J 

cent) 

(per cent) 

(per cent) 

6A 

21 

Steel, double 
slots 

DC 

0.8 

26.5 

- 92 

8.5 




7A 

21 

Steel, double 

Alnico 










slots 

magnet 
at bottom 

None 

2.3 

- 90 

8 

Low 

Low 

9 

9A 

21 

Brass, single 

Alnico 

None 

24 

- 95 

5 

Low 

L< )w 

2 



slot 

magnet 
at bottom 








lOA 

21 

Brass, single 

Alnico 

None 

22 

- 85 

5 

15 

15 

19 



slot, spread 

magnet 










hairpin 

at bottom 








lOB 

Oi 
- 2 

Bra.ss, single 

Alnico 

None 

23 

- 87.5 

4 

13 

10 

9 



slot, spread 

magnet 










hairpin 

at bottom 

0.5 

25 

- 83 

6 

27 

29 

17 

11A 

21 

Plane steel 

DC 








IIB 

21 

Plane steel, 
rubber face 

DC 

0..O 

26 

- 86 

7 

25 

24 

8 

19A 

21 

Polystyrene, 
polymerized 
in place 

DC 

0.7 

2.5.1 

- 97 

30 

6 




The general construction characteristics and test 
results of these eight models are listed in Table 5. 
None of the units was outstandingly good. Open-cir¬ 
cuit frequency responses are shown in Figures 90 and 
91. Most responses were ragged, indicating that there 
were several minor resonances associated with the 


of laminated longitudinal vibrators did not equal that 
of well-constructed laminated stacks of the more 
conventional tyj)e. It is concluded, therefore, that 
unless some way can be devised for overcoming its 
natural weaknes.ses, it cannot compete with the con¬ 
ventional forms. 


CONFIDENTIAL 



















Chapter 8 

TUBE-AN1)-F»LATE TRANSDUCERS 


The theory of the magnetostrictive half-wave tube 
or rod vibrator has been treated in an earlier chapter. 
The problem of applying this type of vibrator to 
underwater signaling has been in part a matter of 
securing the proper acoustic loading on the vibrating 
member. A similar problem arises in ordinary loud¬ 
speaker design; the coil-driven cone and or the 
tapered horn are the devices most usually employed 
to give efficient coupling of the vibrating member to 
the air. In the loudspeaker, the desired condition is 
effective coupling over a wide frequency range to 
in.sure undistorted acoustic output. Pattern require¬ 
ments are in general secondary. The problem in 
underwater sound signaling, on the other hand, has 
been largely one of securing high efficiency over a 
limited frequency range with a sharp beam radiation 
pattern. 

Theoretical considerations presented in earlier 
chapters indicate that the first requirement, high effi¬ 
ciency, calls for a mechanically resonant system. The 
half-wave tube or rod meets this requirement. The 
sharp beam pattern requires a surface whose dimen¬ 
sions are large compared with the wave length of the 
radiated sound vibrating as an acoustic piston, that 
is, with the motion of all parts of the surface in phase. 

The device illustrated in Figure 11 of Chapter 1 is 
an early example of the tube-and-plate idea for in¬ 
creasing the area of the radiating surface. Here the 
driv^ers are magnetostrictive tubes, each tube at¬ 
tached to a block or cylinder of metal the height of 
which is a half wave length in the metal of the radi¬ 
ated frequency. The elements are connected by thin 
webs located in a plane that is relatively stationary 
with reference to the driver and radiating faces. The 
suggested dimensions for a cylindrical block of alumi¬ 
num to resonate at 30 kc are a 2-in. diameter and a 
height of approximately 3 in. The specifications state 
that theoretically the driving tube and the driven 
block should have the same natural frequency. The 
formula given for the length of the magnetostrictive 
tube is 


L = 


^ k 

fo '27r ^ 4 


(1) 


where C„ = velocity of sound in the metal of the 
tube, 


fo = resonance frequency, 
k = the odd integers 1, 3, 5, etc.. 


^ . 1 Mo 

d) = tan ^- 

2wf M 


Mo is the mass per unit length of the tube and M the 
mass of the cap plate in which the tube is threaded 
into the re.sonator block. Note that, if M is small 
compared to Mo, (t>/2r approaches ]/i. This means 
that if the attaching means has a negligible mass 
compared with a unit length of the driving tube the 
latter should be a half wave length when driving a 
half-wave resonator. 


8.1 TUBE-AND-CYLINDER FULL-WAVE 
OSCILLATOR 

Two experimental transducers embodying the idea 
suggested in Figure 11 of Chapter 1 were built at 
Harvard Underwater Sound Laboratory [HUSL]. 
However, instead of relying on deep slots in a half¬ 
wave plate to afford mechanical isolation between 
elements, as in Figure 11 of Chapter 1, each element 
consisting of a half-wave magnetostrictive tube vi¬ 
brator and a half-wave brass cylinder was built 
.separately. These elements were .supported at the 
nodes of the half-wave cylinders by being press-fitted 
and .soldered into holes in a steel plate. Nine¬ 

teen of the.se elements w'ere a.s.sembled in a circular 
array to which a rubber face was molded, as .shown in 
Figure 1. The transducer was designed to have a 
re.sonant frequency of about 64 kc and to have a radi¬ 
ation pattern whose main lobe was 20 degrees wide 
6 db down from the maximum with side lobes at least 
30 db below the maximum of the main lobe. 

These units did not meet the particular need for 
which they were designed but their constmction 
yielded certain useful information on the behavior of 
composite elements intended to operate as full-wave 
oscillators. The single elements, one of which is .shown 
in detail in Figure 2, were carefully tuned by turning 


CONFIDENTIAL 


223 


rUBE-AND-FLATE TRANSDUCERS 


22 i 


down the l)ra.ss c.yUnder to the same resonant fre- 
ciuency, 65.25 ke, to within 0.1 kc. A second mode of 
vil)ration appeared with maximum response at 50 kc. 
Impedometer measurements on the sei)aratc elements 
showed a potential efficiency at this lattei' frequency 
of about 34 per cent, with a mechanical Q of 31. 

The assembled unit, however, showed an efficiency 
of only 5 per cent. This loss is ascribable partly to 
lack of exact phase-matching among the elements in 
the steel plate and partly to the damping action of 
the rubber that intruded into the crevices between 
the brass cylinders. 


the high values of the mechanical Q and their rela- 
ti^'el 3 " low efficiencies. 

8.2 TUBE-AND-CONE HYDROPHONE 

Figure 3 shows a hydrophone of this type, which 
was developed for a special use at HUSL. It con¬ 
sisted essentially of a cone of brass or aluminum, the 
l)ase of which was the radiating surface. The cone was 
driven by means of a magnetostrictive tube attached 
to its vertex. Specifications called for a railiation pat¬ 
tern 90 degrees wide () db down from tlie maximum, 



The main lobe of the radiation jjattern met the 
design requirement of 20-degree width at the G-db 
point, but the side lobes were down only about 15 db. 

As was to be expected, it was found that the reso¬ 
nance frequencies of the individual elements were de¬ 
pendent more on cylinder length than on the length 
of the nickel tube. Even the variations in the mechan¬ 
ical properties of different samples of brass were great 
enough to make (luite appreciable differences in the 
resonant frequencies of different elements, though 
these were made to the same dimensions with all 
possible accuracy. In addition to high mechanical 
los.ses in this particular design, the practically open 
magnetic circuit resulted in magnetization of the 
nickel tubes by the Alnico magnets considei’ably be¬ 
low the optimum. 

Other experimental units of the full-wave oscillator 
type tried at HUSL proved disappointing, because of 


with a maximum sensiti\'ity in the neighborhood of 
20 kc. The pattern requirement dictated a diameter 
of about 3 in. for the base of the cone, and space 
limitations dictated a cone height of 2}/^ in. The 
driving tube had a " ith a wall thickness of 

0.015 in. and was made of soft-annealed nickel. Its 
I)ermeability was 40 to 50 when polarized with an 
Alnico I or Alnico II magnet ^iq in. in diameter, 1^ 
in. long, with a pole strength of about 40 cgs units. 
The tube was slotted to reduce eddy-current losses 
and the magnet was placed about midway within the 
tube. A cone of these general dimensions has a reso¬ 
nance at 27 kc in addition to the 20-kc resonance. 

In the particular use for which this hydrophone was 
intended, a maximum voltage outi:)ut was desired to 
be fed to the grid of an amplifier input tube. The 
pickup coil consisted of 5,000 turns of single cotton- 
covered No. 33 enameled cojiper wire. The high side 


CONFIDENTIAL 
























































































































































FOUR-TURE IIYUKOPHONE 


225 


of this was connected in series with a loading coil of 
0.23-h inductance at 1,000 cycles. The distributed ca¬ 
pacity of the 2.5 feet of two-conductor shielded-cable 
connection to the amplifier served to parallel-tune the 
loading coils at a jieak frequency of 20 kc. The open- 
circuit sensitivity of the hydrophone thus terminated 
was ol the order of — 55 to — 60 db vs 1 volt per dyne 
l)er sq cm. \\ ith brass cones, the measured Q was 
about 60, whereas an aluminum cone giving approxi¬ 
mately the same sensitivity showed a Q as low as 30. 

In Table 1 are shown computed values of sensitiv- 

T.\ble 1. Computed values of sensitivity and effi¬ 
ciency for diffei'ent comlfinations of brass cones and 
driver. Resonance frequency 19 kc; radiating face 
3 in. in diameter. 


Hpig;ht 

Ere- 


Sensitivitv 



of cone 

quencv 


db /1 volt ’ 



(inches) 

(kc) 

Driver 

dyne/cm- 

n • 

Eff 

2.75 

19 

0.015-in.slotted tut)e 






2.32 in. long 

— 05 

44 

0.10 

2.75 

19 

O.OlO-in. slotted tulx- 






2.35 in. long 

- 00 

37.5 

0.075 

2.75 

19 

0.00.5-in. laminations 






0.2 cm- cross sec¬ 
tion 2.22 in. long 

- .50 

8.5 

0.30 

2.75 

19 

0.00.5-in. laminations 






0.02 cm^ cross sec¬ 
tion 1.83 in. long 

- 44 

80 

0.02 


ity and efficiency for different combinations of brass 
cones and driver, all designed to have a resonance 
frequency of 19 kc, with radiating face 3 in. in diam¬ 
eter in each case. 

Figure 4 shows a breakdown of a typical cone hy¬ 
drophone into its components. The radiation pattern 
of the hydrophone .set in a pres.sure-release baffle is 
given in Figure 5. 

8 .3 FOUR-TUBE HYDROPHONE 

A later develojiment at HUSL of a hydrophone em¬ 
bodying the tube-and-plate idea is .shown in Figure 6. 
Specifications called for a peak freciuency of 24.5 kc 
with an effective band width of 2 kc and a reception 
pattern having a .single beam 120 degrees to 140 de¬ 
grees wide 10 db down from the maximum. The unit 
was to feed into the grid of the first amplifier stage, 
producing a voltage of —60 db vs 1 volt for a field 
l)res.sure of 1 dyne per sci cm at peak frequency. The 
radiating face was 23 ^^ in. in diameter. 

It was found that the peak response was nearly in¬ 
dependent of diaphragm thicknesses between Yi in. 


and Ya ill- The length of the driving tubes was 2.03 
in., approximately one-fourth of the wave length in 
nickel of sound of the resonant frecpiency. Slotted 
seamless tubing with 0.015-in. wall or rolled tubes 
made from 0.010-in. sheet were used. The diaphragm 
was .suspended by a thin, relativelj" compliant web 



at the periphery in order to produce true piston mo¬ 
tion. This web was in- thick and extended for jd in. 
beyond the diaphragm. Higher sensitivity was shown 
when the compliance ring ])rojected from the lower 
rather than the upper edge of the diaphragm. 

In order to get the desired frequency band width, 
small variations were made in the effective lengths of 
the four tubes. Units having equal length tubes had 
effective band widths of about 800 cycles; units with 
tubes that varied by steps of i (34 in. from 33^2 in- 


CONFIDENTIAL 









































226 


TUBE-AND-PLATE TRANSDUCEKS 


had band widths of 1,200 cycles and, with twice this 
variation, the band width was increased to 2,000 
cycles. 

Experience with the cone hydrophones led to the 
use of silver solder instead of soft solder. With time, 
hydrophones in which soft solder was used frequently 
showed changes in their sensitivity that were believetl 
to be due to the crystallization of the lead in the 
solder. Tubes were of uniform length but their effec¬ 
tive lengths were varied by counterboring holes of 
different depths in the diaphragm. The tubes were 
annealed in hydrogen at a temperature of 900-1000 C 
for one hour and polarized with Alnico magnets 
in. in diameter, magnetized to a pole strength of 40 
cgs units. 

The special termination of the hydroi)hone in the 
particular use for which it was designed is of interest. 
It was specified that the unit shoidd operate into an 
input panel originally designed to terminate a crystal 



hydrophone with high capacitive impedance. This 
jianel consisted e.s.sentially of a 225-mh toroidally 
wound coil and an 0.82-megohm resistor shunting the 
grid of a 6SH7 tube. The choke parallel-tuned the 
capacity of the crystal and the high shunt resistor 


.served to match the injjut impedance to the charac¬ 
teristic impedance of the crystal tran.sducers. The 
method by which a fairly respectable match was se¬ 
cured between the magnetostrictive transducer with 
its inducti\"e impedance and the input provided at 
the panel is shown in Figure 7. The condenser Cj 
parallel-tuned the inductance of the four coils to elec- 



F'igi ke 4. Parts of tiihe-aiid-cone hydroplioiie. 


trie resonance at jteak freciuency, giving an output 
impedance, mainly re.sistive, of about 30,000 ohms. 
The capacitance C is due to the cable (50 to 60 
which reduced the effective inductance of the 225-mh 
input coil. The series condenser Co located inside the 
microphone case served both to block a low-fre([uency 
switching voltage that was impressed acro.ss the first 
stage and to effect the complete timing of the input 
coil. This termination was not ideal, but even with 
the loss of sensitivity due to the broadened response, 
the four-tube hydrophone gave a voltage .sensitivity 
into the grid of the first amplifier stage of from 60 to 


CONFIDENTIAL 



















































FOUR-TUBE HYDROPHONE 


227 



Figure 5. Pattern at 20 kc of tiitie-and-cone hydio- 
phone in [iressnre-relea.se ViafHe. 



k'lGURE 6 . Section of four-element tube-and-plate 
hydrophone. 


()o db below 1 volt for a sound field of 1 dyne per stj 
cm, only slightly less than that of the crystal hydro- 
jihone designed for the same use. 

This case exemplifies a fact that is constantly en¬ 
countered, namely, proper electric termination is a 
prime requisite for satisfactory transducer perform¬ 
ance and this problem for magnetostrictive units that 
are relatively low inductive impedance devices is 
fundamentally different from that for high-imped¬ 
ance capacitive crystal hydrophones. 

The construction of this four-tube hydrophone is 
indicated by the photographs. Figures 8 and 9. These 



- C- SERIES TUNING 
^ CAPACITANCE 
C CABLE CAPACITANCE 

Figure 7. Termination of four-tube magnetostrictive 
hydrophone wlien reiilacing a high-impedance crystal 
hydrophone. 



Figure 8. Components of four-tube hydrojdione. 



Figure 9. Subassembly of four-tube hydrophone. 


units were fairly rugged and coidd stand a reasonable 
amount of abuse without change in their perform¬ 
ance. Pattern and receiving response curves are 
shown in Figures 10 and 11. 


CONFIDENTIAL 






















































































228 


TUBE-AND-PLATK TRANSDUCEKS 


8.1 TUBE AND SLOTTED-PLATE 
PROJECTOR 

Eai'Iy in tlie liistoiy of tlie sonar ])rog:ram at 
HUSL, the need arose for a shai'p beam transducer to 
use as a mechanically rotated receiver. The shaip 
beam reciuirement called for dimensions that were 
large in com])arison with the wave length in water 
of the sound to be recei^•ed. The e.xisting eciuipment 
designed to be used with this transducer operated at 
about 14 kc, corresponding to a wave length in water 
of approximately 4 in. A 12 X 12-in. radiating .sur¬ 
face was thought to be sufficiently large to meet the 



Fioure 10. Patterti at 24.5 kf of foiir-tiihc hjalro- 
plione. 


pattern reciuirement. C'onsiderations of weight sug¬ 
gested a relatively, light tube-dric en jilate. In earlier 
experiments with plates less than Yi in. thick di’iven 
at distributed points, the tendency of such j)lates to 
break into segmented vibrations had been noted. 
These partial vibrations resulted in bad patterns and 
ragged freciuency response. To a\'oid this difficulty 
while still using a relatively light con.struction, the 
jilate was divided into small segments and each seg¬ 
ment was ch-iven by its own tube and coil as.sembly. 

The detailed construction of the unit built is shown 
in Figure 12. The steel diaphragm was in. thick, 
with diagonal slots 3^16 in. wide and Ke 'H- deep milled 
in the back surface, producing 112 square segments 
each 1 in. on a side. A nickel tube in. in diameter, 
3.7 in. long with 0.010-in. wall, was .soldered to each 
segment. The tubes were irolarized with Alnico mag¬ 


nets. Each magnet was held in a wood dowel carried in 
the frame that supports the coils. Eac'h coil consisted 
of 104 turns of No. 20 wire and the coils in each half 
were connected in series. Separate leads were brought 
out from each half. 

On the a,s.sumi)tion that the Ke-in. web l)etween the 
sc'gments effects mechanical isolation betw'een sec¬ 
tions, each tube may be treated as a (piarter-wave 
vibrator mass loatled at one end, and the analysis 
given in ('hapter 3 should apply. If the coupling be¬ 
tween .segments is negligibly small, all parts of the 



21 22 23 21 25 2<r 2 7 28 


FREOUENCY IN KC 

Figure 11. Freciuency response of four-tuhe liyclro- 

phone. 

plate should lie driven in i)hase, and true piston mcj- 
tion should result. If these conditions are realized, the 
jiattern and freciuency respon.se should be unaffectc'd 
by segmental vibrations. From Figure 17 in Chapter 
5 this transducer, which is 3 wave lengths on a side, 
would be expected to show a pattern with the main 
lobe 17 degrees wide at the —3 db points and 22 de¬ 
grees wide at the — (3 db points, with the minor lobes 
down 13 db from the main lobe. The mea.sured pat¬ 
tern of Figure 13 shows a fair agreement with the 
theoretical values, although the iiattern as a whole is 
not gratifying. The 12 X r2-in. tube and slotted- 
plate i)rojector was the first attemiit of HUSL to 
build a projector of this type. Though its performance 
was not outstanding, it served a very useful purpose 
in the general development jn-ogram, since it was the 
finst transducer on which an analysis was made based 
on both impedance and acoustic measurements. Im¬ 
pedance curves in air and in water ai-e sliown in 
Figures 14 and 15, and the derived motional imped¬ 
ance circles in Figures 16 and 17. The rather large 
deviations of the measured points from the plotted 
curves will be noted. This is exjjlained by two sources 
of experimental error that were not rccognizc'd in the 


CONFIDENTIAL 













































Tl’BE AND SL0TTP:D-1»LATE PROJECrrOR 


229 



330" 0" 30" 



Figure 13. Pattern of 12 x 12-in. transdueer. 


early stages of this work. The first was due to lack of 
precision in the assigned value of the frequencies, and 
the second arose from the variation with frequency 
of water-loading due to the standing waves in the 
tank. 



Figure 14. Impedance curve of 12 x 12-in. trans¬ 
ducer in air. 


CONFIDENTIAL 



































































































































































TUBE-AND-PLATE TRANSDUCERS 


2.-$0 


8.5 QC PROJECTORS 

The tube-and-plate projectors used l)y the Navy 
for echo-ranging are designated as the QC type; in 
this classification are included a large number of 
subtypes all operating on the same general principle 
Init with various modifications in detail. The QCb 
illustrates the construction used. It is designetl to 
operate at 20 kc and is housed in a spherical chamb(‘r 



lO 20 30 40 50 

R IN OHMS 


Figure 15. Impedance curve of 12 x 12-in. trans¬ 
ducer in water. 

19 in. in diameter with a front half of stainle.ss steel 
0.040 in. thick. The rear portion of the housing is of 
heavy cast iron with internal ribs. Both front and 
back jiortions are fastened to a heavy midsection of 
cast iron in which the projector itself is mountetl. The 
latter is a steel plate 1 in. thick and 16 in. in diameter 
to which are firmly attached 608 nickel tubes each 
0.25 in. in outside diameter with 0.025-in. wall. Each 
tube extends 2.563 in. from the face of the plate. The 
diaphragm is held in the housing by a gasketed 
clamping ring. The space between the front face of 
the diaphragm and the thin front cover of the hou.s- 



Figure If). Motional impedance circle of 12 x 12-in. 
transducer in air. 



R IN OHMS 

Figure 17. Motional impedance circle of 12 x 12-in. 

transducer in water. 

ing is filled with a mixture of ethylene glycol and 
water. 

All the tubes in each vertical row have coils with 
the .same number of turns, but the number of turns 
l)er coil increases from a minimum for the outer rows 
to a maximum for the center rows. The coils on each 
half are connected in .series, with the two halves con¬ 
nected in parallel. A 75-volt d-c power source supplies 
6.8 amp of polarizing current through a choke coil 
in a filter junction box. Tuning condensers tune out 
the reactive component of the impedance, giving a 
jiure resistance of approximately 100 ohms at 20-kc 
re.sonance. 


CONFIDENTIAL 












































































STUDIES AT BELL TELEPHONE LABORATORIES 


231 


«.6 STUDIES AT BELL TELEPHONE 
LABORATORIES 

A study of the QCL transducer was made at the 
Bell Telephone Laboratories^'*; results appear in a final 
report to the Bureau of Ships on Task No. 4B. The 
work on this task was directed to the development 
of a magnetostrictive i^rojector unit interchangeal)le 
with the standard QC' projector but with greater 
band width in order to eliminate the sharp tuning 
required for efficient operation of a highly resonant 
transducer. A comprehensive theoretical study of the 



Figure 18. Mounting for small-scale tests of tube- 
and-plate transducers (BTL). 


tube-and-plate type of tran.sducer was made. This 
was supplemented by the construction and testing of 
a considerable number of small-scale model units and 
vdtimately bj^ a full-sized unit, XI-100, embodying 
the results of the theoretical and experimental 
studies. 

For the small-scale tests the models were mounted 
in a test chamber of the type shown in Figure 18. 
This accommodated a diaphragm 4% in. in diameter, 
mounted in the front flange and clamped between 
rubber gaskets by means of the clamping ring shown. 
Measurements were made in an absorbent-lined 
tank.”* The power input was either 1 watt or 0.1 watt, 
and response and pattern measurements were made 
at a distance of about 14 in., using a calibrated pre.s- 
sure gradient hydrophone. A typical model is shown 
in Figure 19. The tube-and-plate a.s.sembly for the 
full-scale unit is shown in Figure 20. 



Figure 19. Small-.scale experimental model tube- 
and-plate tran.sducer (HTL). 



' 'bj ' ‘ ’ 


FiouRE 20. Tube-and-plate assembly for XI-100 ex¬ 
perimental QC projector (BTL). 

Descriptive data with measurements of perform¬ 
ance are given in Table 2. Construction details, which 
may materially affect performance, are given in Fig¬ 
ure 21. Note that the tubes were force-fitted into the 
thicker plates by means of taper plugs and were 
brazed onto the thin steel plate. The coils, impreg¬ 
nated with bakelite resin, were bonded directly to the 
tubes. In the QC’L the coils are wound on thin-walled 
bakelite tubes, which slip loo.sely over the nickel 


CONFIDENTIAL 












TUBE-ANI)-I‘LATE TRANSDUCERS 


2:}2 



Table 2. Data on BTL tube-and-plate experimental model projectors. 


Model 

Material 

Thick¬ 

ness 

(inches) 

No. 

Ma¬ 

terial* 

Wall 

(inches) 

OD 

(inches) 

A,t 

A, 

Bias! 

Fn‘q 

Band- 

\viclth§ 

Eff 

(db) 

Eff 

(per cent) 

XI-10 

Magnesium 

1 

21 

Ni 

0.010 

3 

0.020 

DC' 

18..5 

1.9 

- 9.4 

11.5 









PM 

18..5 

1.7 

- 8.5 

14. 

XI-15 

Magnesium 

3 

4 

21 

V-P 

0.010 


0.020 

D(' 

24.0 

3.2 

-10.0 

10. 

XI-20 

Magnesium 

1 

44 

Ni 

0.000 


0.021 

DC' 

19.0 

2.0 

-12.6 

5.5 

XI-30 

Magnesium 

1 

21 

Pv 

0.010 

2 

0.02() 

DC’ 

20.0 

2.2 

- 7.4 

18. 

XI-40 

Magnesium 

2 

21 

Ni 

0.000 

1 

2 

0.010 

DC 

17.2 

3.2 

-12.7 

5.5 

XI-50 

Steel 

S 

21 

Ni 

0.010 

1 

3 

0.020 

DC’ 

2.5.0 

3.0 

- 9.6 

11. 

XI-60 

Magnesium 

3 

4 

21 

Ni 

0.010 

1 

2 

0.02t) 

DC 

23.0 

2.8 

- 8.3 

15. 









PM 

23.5 

3.5 

- 9.7 

10.5 

XJ-20 

Polystyrenell 

!i 

i' 6 

12 

Ni 

0.012'1 

1 

2 

0.03f) 

DC' 

28.0 

10.0 

-12.7 

5.5 









PM 

28.0 

10.() 

-13.0 

5. 

X.J-30 

Polystyrene 

3 

4 

12 

Ni 

0.000 

1 

2 

0.000 

DC’ 

22.0 


-17.2 

1.7 

XJ-40 

Lucitell 

3 

4 

12 

Ni 

0.000 

1 

2 

0.018 

DC' 

22.5 

7.0 

-11.8 

6.5 


* Ni: nickel; V-P: vanadium-Permendur. S3 db below peak response. 

ratio of cross-sectional area of tubes to that of diaiihragm. !] Diameter of radiating .surfaee is 2.84 inches; for other models, 4 inches. 

+DC; direct current; PM; permanent magnet. ^ 6 layers of tape 0.002 in. thick. 


tubes and rest directly on the plate. In the experi¬ 
mental models, the loading of the tubes by the coils 
lowered the resonant frecpiency appreciably and cpiite 
pos.sibly had some effect on increasing the band 
width. Various inferences are drawn from the data. 
Models XI-10 and XI-20 differ in wall thickness of 
the tubes, 0.010 in. and 0.006 in. respectiv’ely, but the 
closer spacing of the latter yields about the .same 
ratio of cros.s-sectional area of nickel to cros.s-sec- 


tional area of the diaphragm as in the former. The 
band width was the .same for the two, but the 
efficiency of the thin-walled model was about 3 db 
(50 per cent lower). The efficiency of both units is 
lower than the efficiency computed for a clo.sed mag¬ 
netic return path. It was concluded that flux leakage 
materially reduces the effective value of the magneto- 
strictive constant and that this reduction is greater 
for thin-walled than for thicker-walled tubes. A wall 


CONFIDENTIAL 
































































































STUOIES AT BFXL TELEPHONE LABORATORIES 


2:j.i 



thickness of 0.010 in. was suggested as a good com¬ 
promise l)etween the low eddy-current reciuirement 
calling for thin tubes and the desideratum of low flux 
leakage, which calls for thicker walls. 

Model XI-40 represents a .second attempt to use 
the 0.006-in. tubes. Here the tubes are larger, the 
spacing greater than in XI-20, and the decrea.sed 
ma.ss of nickel is partly offset by a diaphragm of half 
the thickness. The efficiencies of XI-20 and XI-40 
are similar, as they should be theoretically, but lower 
than that of the units with the 0.010-in. tubes. 

Motlel XI-60 is like XI-10 but has a thinner dia¬ 
phragm. It shows a somewhat greater band width but 
similar efficiency. BTL ascribes this variation to a 
difference in coil design. In Model XTIO the coil was 
concentrated near the node, whereas in XI-60 the 
coil extended over the lower half of the tube. 

There may be a question as to whether increased 
band width without loss of efficiency is to be as¬ 
cribed wholly to the change in coil design. Increased 
band width with decreased plate thickness is to be 
ex{)ected from both theory and experiment. Decrease 


in the diaphragm thickne.ss moves the nodal plane of 
the tube towards the free end, raising the resonant 
frecjuenc.y. The maximum change of magnetization 
in the tube occurs at the node; therefore, to extend 
the coil along the tube away from the conducting sur¬ 
face of the diaphragm would tend to increase the al¬ 
ternating flux leakage through the coil, hence in¬ 
crease the electromechanical coupling and the effi¬ 
ciency. To follow this line of rea.soning, the greater 
band width of XI-60 as compared with XI-10 would 
be a.scribed to decreased plate thickness, aiul its un¬ 
diminished efficiency to the change in coil design. 
Before conclusions are drawn, however, experiments 
in which the parameters are varied one at a time are 
desiralffe. 

Magnetostrictive tubes of nickel. Permalloy, and 
vanadium Permendur were used. In comparing XI-10 
and XI-30, increases in both bandwidth and effi¬ 
ciency are noted with the Permalloy tubes. BTL sug¬ 
gests that some slight improvement might be ex¬ 
pected in the performance of transducers of the XI- 
100 type with the u.se of 45-Permalloy, which has 


CONFIDENTIAL 










































tube-and-platp: transducers 


2:{4 


higher pcrmealiility and a resulting reduction in leak¬ 
age flux. Analysis of impedance data, however, indi¬ 
cates that this improvement would be very slight. 

A very close agreement is shown between the jier- 
formance data of XI-15 with a ^-in. magnesium dia¬ 
phragm and XI-50 with a diaphragm of j^^-in. steel, 
which indicates that a i)rojector similar in perform¬ 
ance to the XI-100 with a thin steel diaphragm is a 
pos,sibility. However, there is the po.ssibility that 
flexural modes of vibration would be excited in a 
J g-in. steel plate of QC diameter. 

Of the three plastic models, the best performance is 
that of the XJ-40. This is a transducer of simple con¬ 
struction with wide-band response, but its efficiency 
is .somewhat low for an echo-ranging projector. 
Responses of three of these experimental models are 
shown in Figure 22. 

8.7 QC-TYPE PROJECTOR WITH 

M.4GNESIUM PLATE 

The full-scale model XI-100 was similar in tube- 
and-plate construction to the small model XI-10. 
The diaphragm was of cast magnesium alloy 4, ASTM 
specification B-80. The split tubes were made from 
formed .sheet A-nickel 0.10 in. thick, annealed at 
1000 C. Each tube had a inside diameter. 

Tubes, 448 in all, were arranged in sciuare pattern on 
^^-in. centers and were secured in the plate by means 
of a forced fit, using tapered pins. Coils were impreg¬ 
nated with bakelite resin BR-0014 and bonded to the 
tubes. Each coil had 80 turns of No. 25 es wire. The 
housing was essentially the same as that of the QCL. 
Transmitting responses of the XI-100, the QCL, and 
the QCU projectors are shown in Figure 23. 

8.8 COMPARISON OF DIFFERENT QC 

MODELS 

Tables 3 and 4 contain data on QC' projectors that 
have been used by the Navy as well as experimental 
modifications of some of them. Structurally they all 
bear a close family reseml)lancc to the QC’L de¬ 
scribed in an earlier section. A similar resemblance 
is to be noted in their performance data. 

The coils in the QGA'^ units are carried free from 
the tubes and plates, with the wintlings crowded close 
to the motion nodes of the tubes. The permanent 
magnets are tightly fitted at one end within a .soft- 

“ Information on QC’A projectors furnished by E. E. 
Turner, .Ir., of the Submarine Signal Company, Bo.ston, Mass. 



Figure 23. Transmitting re.sponse of three QC-type 
projectors (BTL). 



Figure 24. A.ssemVily detail of tube, coil, and mag¬ 
net in the QG.A projectors (Submarine Signal Com¬ 
pany). 


iron distributing plate with the opposite ends pro¬ 
jecting into rece.sses in the diaphragm plate, allowing 
a small radial air gap between magnets and plates. 
The arrangement is shown in Figure 24. 

In the QCU units,^® the biasing magnetization is 
supplied by heavy Alnico slabs backing the soft-iron 
distributing plate. The return magnetic path is by 
way of the plate and the steel of the supporting ring. 


C(3NFIDENTIAL 











































COMPARISON OF DIFFERENT QC MODEES 


235 


Table 3. Descriptive data on tube-and-plate projectors. 




Plate 



Tubes 


Projector 

material 

thickness 

(inches) 

effective 

diameter 

(inches) 

number 

length 
(inches) 

OD 

(inches) 

wall 

(inches) 

1. qch 

Steel 

1 

15 

608 

2.5 

0.25 

0.025 

2. QGA Type 941 

Steel 

3 

4 

16 

424 

3..58 

0.25 

0.025 

3. QGA Type 942 

Steel 

3 

8 

12 

256 

1.69 

0.25 

0.025 

4. QCU Production 

Steel 

5 

S' 

111 

182 

2.04 



5. QCU No. 1 Experimental 

Steel 

F?) 

111 

152 laminated stacks 0.15 X 0.15 X 2.04, 
diaphragm slotted 

6. QCU No. 2 Experimental 

Steel 

F?) 

111 

Same as No. 5, but diaphragm not slotted 

7. QCU No. 3 Experimental 

Steel 

7 

S 

111 

182 

2.04 



8. XI-100 

Magnesium 

1 

15 

448* 

2.5 

0.63 

0.010 


* Split tubes; all others slotted. 


Table 4. Performance data of QC-type projectors. 


Type 

Resonant 

frequency 

(kc) 

Impedance 

at 

resonance 

Sensitivity 
(db) ‘ 

Directivity 

(db) 

() 

.4, 

A.2 

Band¬ 

width 

(kc) 

Efficiency 
as projec¬ 
tor (db) 

Efficiency 
(per cent) 

QCL* 

20.4 

34 -b i69.5 

- 85 

- 21 

41 

0.066 

0.5 

- 9.5 

11 

QGA Type 941t 

14.8 

120 + /285 

- 76 

- 18.2 

38 

0.037 

0.4 

- 8.0 

16 

QGA Type 942t 

30.5 

130 -h /235 

- 76.4 

- 23.2 

24 

0.04 

1.27 

- 7.5 

18 

Q('U Productionf 

25.4 

33.8 -fill? 

- 80.5 

- 22.5 

80 


0.3 

- 3.8 

42 

QCU No. 1 Experimental! 

24.3 

98 -b i218 

- 69.8 

- 23.6 

81 

0.031 

0.3 

- 3.0 

50 

QCU No. 2 Experimental! 

24.2 

103 -b j235 

- 68.2 

- 23.3 

97 

0.031 

0.24 

- 2.5 

56 

QCU No. 3 Experimental 11 

25.4 


- 81.5 

- 22.5 

100 


0.25 

— 4.5 

35 

XI-100 Experimental 1 

18.5 



- 23.2 

7.4 

0.026 

2.5 

- 9.7 

10.7 


* NDRC Report Sec. 6.1 sr 20-889. .Sensitivity: ref. 1 volt/dvne/cm^. 

t NDRC Report Sec. 6.1 sr 11.30-1626. Directivity (db): 10 log D. 

t NDRC Report Sec. 6.1 sr 1130-1379. -li/.lj: ratio of area of nickel to area of plate. 

§ NDRC Report See. 6.1 sr 1130-2138. 

II BTL Report on Task -IB, BuShips No. NX sr 46932. 


It will be observed that in all projectors of this type 
the reluctance of the magnetic path for the a-c flux 
is high, because of the low permeability of Alnico. 
Moreover, high losses are to be expected because of 
eddy currents induced in the massive metal of the 
plates. 

Experimental QGU Models 1 and 2 (Figure 25) had 
laminated stacks instead of tubes as the driving ele¬ 
ments. These were soldered to lugs that .screwed into 
the diaphragm plate. In Model 1, the plate was di¬ 
vided by milled slots into square segments each about 
IH X in. Each segment carried four stacks, to 
which coils were cemented directly. In Model 2 the 
diaphragm was not slotted. 

As has been noted, the XI-100 experimental vari¬ 
ant is distinguished by having a 1-in. magne-sium 
plate and thinner-walled tubes with attached coils. 
The magnetizing bias was given by d-c current. 

Inspection of Table 4 disclo.ses a fairly definite cor¬ 
relation between sharpness of resonance and effi¬ 
ciency. For Q’s of 40 or less, efficiencies at resonance 



Figure 25. Plate and laminated stack assembly of 
experimental QCU projectors. 


CONFIDENTIAL 



























































236 


TUHE-AND-I'LATE TRANSDUCERS 


lie between 10 and 20 per cent, while the higher 
efficiencies are associated with Q’s of 80 to 100. These 
\’alues are typical of the general performance of pro¬ 
jectors of this type and would seem to be inherent in 
the low electromechanical coupling of the design. 
C'alculations cited in the BTL report indicate values 
for this quantity one-tenth to one-third as great as 
would be shown if a closed magnetic circuit were a.s- 
sumed. 

8.9 MAGNETIC CIRCUIT IN TUBE- 
AND-PLATE TRANSDUCERS 

Various methods of producing the biasing magnet¬ 
ization of the magnetostrictive tubes have been indi¬ 
cated in previous sections. Perhaps somewhat more 
detailed consideration should be given to the mag¬ 
netic circuits of these methods. 

In the earliest tube-and-plate transducers, mag¬ 
netic polarization was secured by passing d-c current 
through the windings. In the simplest case, the return 
path was through the air outside the tube. The reluc¬ 
tance of the thin-walled tube and the air path is con¬ 
sequently high, and more than 80 ampere turns per 
inch of tube are needed to give the recjuired d-c mag¬ 
netization of the nickel. This may be reduced by 
allowing the free ends of the tubes to project into 
holes in a steel plate (without touching it), so that 
the d-c path consists of all the tubes in parallel, the 
steel sides of the housing, and the steel diaphragm 
plate. This method has the added advantage that the 
polarizing flux is parallel to the direction of strain in 
the region of the node near the plate where the 
strain is maximum. 

When the polarization is supplied lyv small j^erma- 
nent magnets placed inside the tube, the pole nearest 
the plate should extend as far as possible below the 


nodal plane, so that the polarizing flux at the node 
may be as large as possible and parallel to the axis 
of the tube. Eddy-current losses in the magnet can 
be made negligible by copper coating to supply an 
eddy-current shield. 

Another method of using small magnets is indi¬ 
cated in Figure 24. Here a single magnet is placed at 
the center of the square array of the four driving 
tubes that surround it. The extension of the magnets 
into the rece.s.ses in the diaphragm plate decreases 
the reluctance of the d-c flux path and also reduces 
the eddy currents that would otherwise be generated 
in the plate due to its high frequency motion. 

Where the polarization is supplied by Alnico slabs 
as in the QC’U, the Alnico is polarized in the direction 
of the tube length after the transducer is a.ssembled. 
The polarizing flux threads through all the tubes in 
parallel, through the distributing plate, the Alnico 
magnet, the steel housing of the transducer, the steel 
diaphragm, and back through the tubes again. Ob¬ 
viously the distributing plate must be magneticallj' 
isolated from the steel housing, otherwise onlj" a 
small portion of the total Hux would pa.ss through 
the tubes. 

Because of the shielding effect of eddy currents 
in the tubes, at high frequencies their effective cross- 
sectional area is less than their actual cro.ss section. 
This effect has been discussed in Section 3.1 of 
Chapter 3, where it is shown that slotting the tubes 
gives a higher degree of electromechanical coupling 
from a given cro.ss section of nickel. It has been sug¬ 
gested that some decrease in the reluctance of the 
return path for the a-c flux can be effected by at¬ 
taching small packets of thin laminations of highh’- 
permealde material, such as silicon steel, to the out¬ 
side of the windings with the length of the packet 
parallel to the tubes. 


CONFIDENTIAL 



Chapter 9 

MEASUREMENT OF ELECTRICAL CHARACTERISTICS 


9.1 INTRODUCTION 

Much of the performance data of a mechanically 
resonant transducer can be most readily obtained 
from the locus of its vector impedance or admittance. 
With a large program of developmental work on 
transducers such as the Harvard Underwater Sound 
Laboratory has carried on, facilities for making reli¬ 
able electrical measurements should be maintained. 
This chapter includes the measurement technicpies 
employed and the design and construction of the 
electrical measuring equipment u.sed at HUSL. 

In the fall of 1942, several of the HUSL staff were 
assigned the task of making electrical measure¬ 
ments on the various transducers being developed. 
This work consisted mainly of the measurement of 
the electric impedance of these tran.sducers with both 
air and water loading. The water loading was effected 
by immersing the transducer in water in a steel tank 
9 ft long, 4 ft wide, and 23^ ft deep. General Radio 
Company’s Type 516-C radio-frequency bridge with 
considerable acce.ssory apparatus was first u.sed in 
making the.se measurements. Under these conditions 
two sources of large error appeared. The wide range 
of impedances to be mea.sured required the use of e.x- 
terna! variable resistance and capacitance standards 
with the bridge, and the capacities of these boxes to 
ground could not be compensated. Furthermore, re¬ 
flections occurring at the steel walls of the tank gave 
rise to standing wave patterns that caused significant 
error in the ajjparent impedance of the tran.sducer. 

In June 1943, an ab.sorbent-lined tank was re¬ 
ceived from the Bell Telephone Laboratories ami 
proved to be a considerable improvement over the 
steel tank.^® Simultaneously, an impedance bridge 
designed to replace the GR bridge was constructed 
and a.s.sembled in a console. Completed in August 
1943, this bridge was of the .series-tuned arm, equal- 
ratio arm, Wheatstone type. Since some error and 
inconvenience (especially in the measurement of im¬ 
pedance with negative pha.se angles) are inherent in 
this bridge circuit, a similar bridge with a parallel- 


tumal arm was built. This bridge was finished in 
March 1944. 

When the absorbent-lined tank was received, the 
necessary measuring equipment for obtaining pat¬ 
terns, frecpiency responses, and sensitivities of hydro¬ 
phones was built with the hope of taking .some of the 
work load from the HUSL Charles River barge. 
However, the tank proved too small for most of the 
tran.sducers being tested, so that it was u.sed chiefly 
in making mea.surements on developmental elements 
and transducers. 

When HUSL began the construction of .several 
types of multi-element tran.sducers, it became neces- 
.sary to test each of the individual elements. The 
conductometer was devised in October 1944 to provide 
a quick and accurate measurement of the impedance 
and resonant frequency of each element in air. The 
vector impedance locus plotter [VILP],®“ built in Febru¬ 
ary 194.5, grew out of the experience gained in build¬ 
ing the conductometer. This device traces on a cath¬ 
ode-ray tube the vector impedance locus of a trans¬ 
ducer (or any other impedance). It was hoped that 
with experimentation it could be made accurate 
enough to replace the bridges for impedance determi¬ 
nation in all except the most precise measurements. 

9. 2 IMPEDANCE MEASUREMENTS 

9. 2 . 1 General Requirements 

Determination of the locus of the terminus of the 
vector impedance Z = R -\- jX requires mea.sure- 
ment of R and A' at a number of frecpiencies; simi¬ 
larly the determination of the locus of the vector ad¬ 
mittance 1' = Gr -b jB requires the measurement of 
G and B. The value of information derived from these 
loci is proportional to the accuracy, reliability, and 
rapidity achieved in measurements of the quantities 
R, X, G, and B. 

The nature of the loci and the information to be ob¬ 
tained therefrom, as well as the physical character¬ 
istics of the transducers and the conditions under 


2:{7 


CONFIDENTIAL 


238 


MEASURKMENT OF ELECTRICAL CHARACTERISTICS 


which they are to be measured, impose certain re¬ 
quirements on the method of making satisfactory 
measurements. These requirements are listed as fol¬ 
lows. 

Impedance Range. Measurements must be made of 
both resistance and reactance from 0.1 ohm to 10,000 
ohms. The impedance loci of Figures 1, 2, and 3 
illustrate the manner in which R and A' may vary 
with frequency. 


350- f 




R IN OHMS 


Figure 1. Impedance locus of magnetostrictive trans¬ 
ducer in air. 

Reactance Sign. Measurements must be made of 
both positive and negative reactances over the above 
range. With a change in frequency the reactance of a 
given transducer may remain positive, as shown in 
the magnetostrictive transducer of Figure 1; or may 
remain negative, as shown in the crystal transducer 
of Figure 3; or may change from positive to negative, 
as shown in the transducer of Figure 2. Because of 
the frequent occurrence of such a change in sign, the 



0 100 200 300 400 500 600 


R IN OHMS 

Figure 2. Impedance locus of magnetostrictive ring 
stack in air. 



R IN OHMS 


Figure 3. Impedance locus of mechanically resonant 
crystal transducer in air. 

operations required to change from the measurement 
of inductance to the mea.surement of capacity .should 
involve a minimum of alterations in method and ap¬ 
paratus with no loss in time or accuracy. 

Frequency Range. ^Measurements must be made 
over the frequency range from 1 kc to 100 kc. Al- 


CONFIDENTIAL 




























































































































IMPEDANCE MEASUREMENTS 


239 


though the resonant fretiueneies of most of the trans¬ 
ducers fall within a smaller range, the fletermination 
of the core or clamped impedance recjuires measure¬ 
ments at frecpiencies considerably above and below 
resonance. 

Accuracy. The measurements of both R and X must 
involve errors no greater than 1 per cent. 

Ease of Operahon and Computation. The measure¬ 
ments must be made easily and rapidly, and the 


transducer in water. The conditions of measure¬ 
ments can be stated definitely enough to insure re¬ 
producible results only if one terminal of the trans¬ 
ducer is grounded. 

Superposed Direct Current. The measurements must 
sometimes be made with direct currents as high as 20 
amp flowing through the transducers. This neces.si- 
tates grountling one terminal. 

Several methods of measurement can be found 




Inductive Unknown 
At Balance 

Rx = R 

I 

X, =-T 

X oi C 

Figure 4. 


Capacitive Unknown 
At Balance 
R, = R 

~ (J C 

Impedance bridge. 


operations involved in obtaining R and X from the 
observed data must require little time and effort and 
no sacrifice in accuracy. Because of the complexity 
of the loci (Figure 1), it is necessary to plot the locus 
as the measurements are made, in order to select 
those frequencies which will best define the locus 
with a minimum of measurements. For this reason, 
the ease and speed with which the loci can be de¬ 
termined are dependent on both the measuring opera¬ 
tions and the computation and plotting operations. 

Grounding the Unknown. The measurements must 
lie made with one terminal of the unknown imped¬ 
ance grounded. The capacity to ground is not only 
large but variable, becau.se of the large physical size 
of many transducers, the use of long cables with 
them, and the necessity for measurements with the 


that .satisfy these reiiuirements in part, but it is diffi¬ 
cult to satisfy all the requirements by a single 
method. 

9 . 2 . 2 . Measurement by Null Methods 

Bridge ^Methods 

Types of Bridges. Consideration of the foregoing re¬ 
quirements results in the following choice of methods. 
The use of a null rather than a deflectional method 
is demanded by the accuracy required over a wide 
impedance range. Conventional bridge methods are 
applicable if considerable care is taken to remove 
sources of error. The .superiority of variable capaci¬ 
tors over variable inductors both in range and in the 
magnitude and variation of residuals suggests that 


CONFIDENTIAL 




2i0 


MEASUREMENT OF ELECTRICAL CHARACTERISTICS 


reactances l)e measured in terms of a capacitance 
standard; satisfactory standards of cajjacitance and 
resistance are available to cover the recpiired range of 
impedance and frequency. Measurements at super¬ 
sonic frequencies, as well as ea.sy operation, require 
that the bridge network be simple and symmetrical 
in order that the residuals may be controlled or 
eliminated. This involves the use of a ratio bridge 
rather than a product bridge and, in particular, an 


attention must be paid to the residuals in order to 
obtain accurate values of resistance and reactance 
with the resonance britlge. 

For the mea.surement of the impedance of induc¬ 
tive unknowns, the series-resonance bridge of Figure 
4 is convenient. Here three of the branches are re¬ 
sistances and the fourth is a series-resonant circuit 
composed of the unknown and a variable conden,ser. 
When the ratio arms r are equal and balance is ob- 



Induclive Unknown 


Capacitive Unknown 


At Balance 


At Balonce 


G 


X 


I 





_l_ 

R 


B 


X 


_l_ 

W Lx 


CitC 


B,(:-wCx = -wC 


Figure 5. .\dmittance liridge. 


equal-arm ratio bridge. In .such a bridge circuit the 
unknown is compared directly with the standard, so 
that the bridge can be made direct-reading in terms 
of a resistance and capacitance equivalent to the un¬ 
known. Most of the residuals can be counterbalanced 
simply and permanently so that they do not affect 
the reading of the bridge; the others can be made 
negligibly small or can be offset by a constant cor¬ 
rection. 

The requirement that both resistance and reac¬ 
tance be measured to the same accuracy and prefer¬ 
ably with a single balance of a bridge network re- 
(juires the u.se of a resonance bridge. Since the resid¬ 
uals of a bridge network have more effect on the re¬ 
sistance measurement than on reactance, careful 


tained by adjusting R and C, the variable standarrl 
resistor R reads directly the series resistance R^ of the 
unknown, while the reactance of the variable con¬ 
denser C is equal to that of the unknown A'^.. Thus 
only the calculation of the reactance from the value 
of C is nece.ssary to tletermine the reactance of the 
unknown. Even though the ratio arms r are equal, 
the bridge network is not actually .symmetrical be¬ 
cause there is no point in the branch containing the 
variable resistor R to correspond to the junction 
point of the variable condenser C and the unknown. 
Stray capacities from this junction point may cause 
large errors, and, because of the lack of symmetry, 
compensation for these capacities is difficult. The 
form of bridge is convenient for measurements with 


COXFIDENTIAL 




IMPEDANCE MEASUREMENTS 


2tl 


superi)osecl direct current, since the tuning con¬ 
denser C serves to block the direct current from other 
branches of the Ijridge network. 

For the measurement of capacitive unknowns the 
series-resonance bridge becomes a form of capacity 
bridge by the addition of a condenser C, in series with 
the variable resistor K. The balance is still obtained 
with H and C and the resistor R still reads the series 
resistance Rx of the unknown, but the reactance 
of the unknown is the difference between the react¬ 
ance of C* and that of C. This requires two calcula¬ 
tions and in^■olves a loss in accuracy when the differ¬ 
ence in the reactance is small compared to the mag¬ 
nitude of either C, or C. Although there is in this net¬ 
work a junction point in the branch containing R, 
the network still lacks symmetry because the junc¬ 
tion points in the two lower branches are not equiva¬ 
lent when the bridge is balanced. Since the branch 
containing the unknown suffers no alterations in the 
change from inductance to capacitance measure¬ 
ments, this form of capacity bridge is convenient be¬ 
cause it retains the advantage of the series-resonance 
bridge for mea.surements with superposed direct cur¬ 
rent, and the change in bridges can be made without 
interrupting such a current. 

If the unknown impedance is tuned by a parallel 
conden.ser instead of a series condenser, the network 
becomes the parallel-re.sonance bridge of Figure 5. 
The Ijalance is still obtained by varying R and C, but 
at balance the value of R is now equal to the effective 
parallel resistance of the unknown. Since this bridge 
measures in terms of parallel equivalents, it is con¬ 
venient to express the mea.surements in terms of ad¬ 
mittance rather than impedance. For this reason the 
name admittance bridge has been applied to the 
parallel-resonance bridge and that of impedance bridge 
to the serie.s-resonance bridge. The measurements ob¬ 
tained from either bridge, of course, can be expressed 
as impedance or admittance and the locus plotted 
in either form as desired. 

For the measurement of capacitance the tuning 
condenser C has merely to be connected across the 
resistor R instead of across the unknown. This 
change is easily made and involves no additional com- 
j)onents in the network. The condenser C reads di¬ 
rectly the capacitance of the unknown with the same 
accuracy obtained in inductance measurements. Al¬ 
though, as in the impedance bridge, the change from 
measurement of inductance to measurement of ca¬ 
pacitance involves no changes in the connections 
of the unknown, the admittance bridge in either 


form provides no condenser to block direct current 
flowing through the unknown from entering the other 
network branches. Special provisions must be made 
for measurements with superposed direct current. 

The parallel-resonance or admittance bridge has 
the great advantage of permitting one terminal of 
both R and C, as well as one terminal of the unknown, 
to be grounded. This eliminates the junction point 
which was the cause of asymmetry and the resulting 



difficulties in the impedance bridge network. As con¬ 
nected for the measurement of either inductance or 
capacitance, the parallel-resonance bridge network 
with ecpial ratio arms is truly symmetrical, with all 
the attenflant advantages of symmetry. The chief 
ad\’antage of a symmetrical bridge network is that 
all the residuals (but not the changes in residuals 
with a change in R or C) can be eliminated from the 
mea.surement by means of a preliminary balance of 
the bridge with the unknown disconnected. Thus all 
measurements become, in effect, substitution meas¬ 
urements, with accuracy limited by the accuracy of 
the variable standards. 

In the measurement of inductance with either the 
impedance or admittance bridge, the lower limit of 
inductance that can be measured at a given fre- 
(piency is determined by the maximum capacity 
available to tune the inductance; this maximum is 


C(3NFIDENTIAL 









242 


MEASUREMENT OF ELECTRICAL CHARACTERISTICS 



CONFIDENTIAL 















































IM PED ANCE M EASE REM ENTS 


243 


limited to a few microfarads since condensers of low 
dissipation are reciuired.The ujjper limit of reactance, 
inductive or capacitive, is fixed in the impedance 
bridge bj' the errors due to residuals that cannot 
readily be eliminated from that network; in the ad¬ 
mittance bridge this limit is determined by the 
accuracy of the standards employed. In both bridges 
the resistance is limited by the range of the decade 
resistor. In the impedance biidge the limit imposed 
In’ error due to dissipation in the condensers may .set 


source, and the detector are all equal to the imped¬ 
ance being measured. Howe\’er, large deviations from 
this optimum condition can be tolerated in practice, 
since by the u.se of amplification in the detector the 
sensitivity of the bridge can be made more than ade- 
(luate for the required accuracy of mea.surement. 
Hence the magnitude of the ratio arms need not be 
varied, and fixed resistors with accurately matched 
impedances can be used effectually as the equal-ratio 
arms. 



Figure 8. Detector voltage vs bridge unbalance ratios (inductive unknown). 


the lower limit of accurate resistance measurement 
above that impo.sed by the range of the decade. In the 
admittance bridge, which measures equivalent paral¬ 
lel resistance, the upper limit of the decade may not 
be .sufficiently high, but the u.seful range can be ex¬ 
tended by shunting the unknown with a known 
value of resistance. 

^^’ith either the admittance or impedance form of 
eipial-ratio bridge network, the .sensitivity is maxi¬ 
mum when the impedances of the ratio arms, the 


Convergence of Balance. Since the ease and speed 
with which bridge measurements can be made de¬ 
pends upon the manner in which the detector voltage 
\ aries with adjustment of the bridge elements, it is 
worth while to investigate the jirocess by which bal¬ 
ance is attained in the two forms of bridges employed 
for tran.sducer measurements. It is particularl}^ im- 
jiortant to determine the manner in which the de¬ 
tector voltage responds to the balance adjustments 
when the bridge is not near balance, in order that the 


COXFIDEXTIAL 




















































































































































































DETECTOR VOLTAGE IN db DETECTOR VOLTAGE IN db 


244 


MEASUREMENT OF ELECTRICAL CHARACTERISTICS 




Figure 9. Detector voltage vs bridge unbalance ratios (capacitive unknown). 


succe.sbiive adjustments required to attain balance 
may be made in the right order to cause the detector 
voltage to converge towards zero rapidly. 

B}' assuming that the detector has infinite imjied- 
ance, as is closely approximated in practice by a 
vacuum-tube voltmeter, for the Wheatstone network 
of Figure 6 the ratio of the detector voltage T' to the 
applied voltage E is 

1 ZiZ^ — Z<iZ^ 

E (Z\ Z<i){Zz -hZi) 

For an equal-arm ratio bridge Zi = Z 2 and 
_ r ^ 1 Z3 - Z4 
E 2Zs-hZ,' 

This equation, applied to the four bridge networks 
used for the determination of impedance and admit¬ 
tance loci, gives the results tabulated in Figure 7. 
The formulas for the magnitude of V. E are the same 
for both impedance and admittance bridge networks, 
but the parameters a, r, and Q are inverted in going 
from one form of bridge to the other. Note that the 


unknown is representtKl as its sei’ies eciuivalent in the 
impedance bridge network and as its parallel equiva¬ 
lent in the admittance bridge network. 

The parameter arepresentstheresistanceunbalance 
ratio and the parameter r the reactance unbalance 
ratio. The parameter Q for both networks is the usual 
ratio of series reactance to resistance. In Figures 8 
and 9 the detector voltage, expressed in a logarithmic. 
\’oltage ratio as 20 log V E, is plotted as a function of 
the.se parameters. The detector voltage is plotted 
logarithmically because the voltmeter used as a de¬ 
tector has variable gain and is in effect a logarith¬ 
mic voltmeter, that is, the meter .sensitiL’ity is in¬ 
versely proportional to the applied voltage. The 
values of 1 and 10 have been chosen for the param¬ 
eter Q as .sufficient to illustrate the effect of the Q 
of the unknown on the convergence. 

The conclusions to be drawn from the curves of 
Figures 8 and 9 are as follows: 

The reactance adjustment should be made first, 
since there is a better minimum of detector voltage 
when the reactance is varied with a resistance un- 


COXFIDENTIAL 





















































































































































































2i5 


IMPEDANCE MEASUREMENTS 



Figure 10. Tabulation of convergence equations for actual bridge networks. 


balance than when the resistance is varied with a 
reactance imbalance, especially with a high Q. 

The initial value of a should be less than unity 
rather than greater for rapid convergence. This 
means that if the initial setting of R is not close to 
the balance value, that is, to the resistance P, then 
for the imjiedance bridge the setting of R should 
preferably be less than P and for the admittance 
bridge the setting of R should be greater than P. 

The actual bridge circuits of Figures 12 and 16 
differ somewhat from the simple networks of Figure 
7. The principal difference is due to the shunting of 
the two lower branches of the bridge networks by the 
resistances contained within the Leeds & Northrup 
ratio box for the purpose of obtaining a conductance 
balance. The liridge networks for inductive un¬ 
knowns become those of Figure 10 if these shunting 
resistances are included. The value of the resistors 
M in the L & N ratio box is 4,000 ohms. 

If the resistors M are equal they do not affect the 
balance conditions for the network, but their effect 


on the convergence is apparent in the appearance of 
the factor /3 in equations for the magnitude of V/E. 
The admittance bridge network of Figure 10 can be 
simply reduced to the form of Figure 7 by con¬ 
sidering the resistors M as parts of P and R. The 
curves of Figures 8 and 9 can thus be applied if the 
primed values of a and Q are converted to the un¬ 
primed values for which the curves are plotted 
through the relations 

«' + d 

a — - 

d + 1 

and 


The effect of M on the impedance bridge network 
is more complex, since the shunt resistor M cannot 
be considered as a constant series-equivalent re¬ 
sistance added to P if the reactance is varied. As the 
magnitude of P becomes comparable to M, that is, 
d —+ 1, the effect on the convergence is considerable. 


CONFIDENTIAL 

































246 


MEASUREMENT OF ELECTRICAL CHARACTERISTICS 



Figure 11. Detector voltage vs bridge unbalance ratios {B = 1). 


as shown in Figure 11. However, if the use of the 
bridge is confined to unknowns of such low imped¬ 
ance that P is small compared to M, that is, ^3 < < 1, 
the effect of M is negligible and the curves of Figures 
8 and 9 are applicable. 

An apparent advantage of the impedance bridge 
network over the admittance bridge is the ease of 
obtaining initial balance. This can be attributed to 
the fact that the concept of impedance is more 
familiar to the operator than that of admittance and 
that the series-equivalent low-frequeue}^ a-c re¬ 
sistance is close to the value of the d-c resistance. 
These combine to make it easier, with the impedance 
bridge, to set the initial value of the decade resistor 
R close to the balance value. For rapid convergence, 
the decade setting shoidd be low rather than high in 
the impedance bridge. This condition is readily ful¬ 
filled, since the decade range exfends down to zero. 
In the admittance bridge the reverse should be true. 
This latter condition is not so readily obtained, be- 
cau.se the decade range is limited to 10,000 ohms at 
the upper end. The parallel-eciuivalent resistance of 
the unknown impedance is often above 10,000 ohms, 
so that unless the unknown is shunted down to the 
range of the decade resistor the setting of the decade 
must necessarily be low and the tiridge cannot be 
brought into balance by adjustment of the decade 
alone. 

The HUSL Impedance Bridge. An impedance 


LQN Rotio Boi 



bridge of the type shown in Figure 4 was built at 
HUSL. A complete circuit diagram of this bridge is 
shown in Figure 12, a sketch of the bridge console 
showing the arrangement of components in Figure 13, 
and a photograph of the bridge console and acces.sory 
apparatus in Figure 14. 


CONFIDENTIAL 





































































































IMPEDANCE MEASUREMENTS 


247 



Figure 13. Sketch of impediince bridge coasole. 


A Leeds & Northrup, Camphell-Shackeltoii shield¬ 
ed ratio box (No. 1553) contains the two shielded 
and accurately balanced 1,000-ohin resistors that 
comprise the ratio arms r, a double-shielded input 
transformer, and capacitance (Cap and S) and re¬ 
sistance {(r) trimmers for obtaining an initial bal¬ 
ance. The connections to the other two bridge arms, 
to the oscillator, and to the detector are conveniently 
made from shielded terminals on the ratio box. The 
variable resistance /? is a Leeds A Northrup six-dial 
shielded resistance box (No. 4764) with a range of 
11,111.1 ohms in 0.01-ohm steps. The variable ca¬ 
pacitance C is composed of the parallel capacitors 
C[), an L & N three-dial shielded mica capacitor 
(No. 1071) with a range of 1.11 ni in 0.001-yuf steps, 
and Ca, a ■ General Radio variable air condenser 
Type 539-C with a nominal capacitance of 60-2000 


Hfii. The GR condenser has been provided with a 
second shield for reasons to be discussed below. The 
trimmer conden.ser Cr consists of a 200-/:x/;if fixed mica 
condenser in parallel with a 300-MMf variable air 
condenser. The trimmer resistor Rt is a variable re¬ 
sistor with a range of 0 to 10 ohms in 1-ohm steps 
constructed from J-^-watt 1-ohm resistors and an 
11-position rotary switch. The other trimmer re¬ 
sistor Rt is a GR Type 669 compensated slide-wire 
resistor, continuously variable from 0 to 1.1 ohms. 
The terminals marked “series conden.ser” permit 
the in.sertion of a GR Type 509 standard condenser 
in series with the resistance R as the capacitance Cg 
required for the measurement of capacitive un¬ 
knowns. For the measurement of inductive un¬ 
knowns these terminals are shorted. These bridge 
components, together with a tuned amplifier de- 


CONFIDENTIAL 
























































248 


MEASUREMENT OF ELECTRICAL CHARACTERISTICS 



Figure 14. Iniptnlaiice bridge console and auxiliary apparatus. 


lector, were assembled in a console, as sliown in 
Figures 13 and 14. Connections lietween components 
have been made witli mishielded bus wires. 

The necessity tor operating the varialtle conden.s- 
ers with botli terminals off ground retiuires that 
considerable care be taken in the control of stray 
capacities from these components to ground. The 
capacity from the high side of the condenser to 
ground (C.i in Figure 15A) shunts the whole arm of 
the bridge, while that from the low side Cb shunts 
oidy the unknown, Z.y. It is ea.sy to compen.sate for 
C.i by an ecpial capacity (V shunting the ojtposite 
arm (Figure 15B), but C« causes an error in the ap¬ 
parent value of Z.Y. Hence it is desirable to have the 
value of ('b known, constant, and as small as jio.ssible 
in order to correct this error or to make it negligible. 
If the shield of the conden.ser is connected to one side 
of the condenser, as it is in the GR variable air con¬ 


denser, and the condenser is connected as in Figure 
15A, the large capacity from the shield to ground is 
Cb, which shunts the unknown. The connection 
shown in Figure 15B makes the cai)acity from shield 
to ground G,i, which can l>e compensated by Cj-, 
leaving only a small value of Cb across the unknown. 
However, in making adjustments of the capacitance 
C, the operator’s hand varies the capacity C.i, which 
makes a fi.xed compensation of G.i impossible and 
the process of determining Iialance very difficult. To 
make the cajiacity G.i definite regardless of the 
position of the operator’s hand, a second, grounded 
shield can be added to the condenser, as in Figure 
15C. Such a shield has been added to the GR variable 
air condenser used in the impedance bridge. No alter¬ 
ations were made in the GR conden.ser other than to 
enclose it in a Dural box, which required adding a 
longer shaft to the vernier control, removing the 


CONFIDENTIAL 











IMPEDANCE MEASUREMENTS 


219 


knob from the dial, and providing terminals on the 
outer case. Since the vernier shaft is electrically con¬ 
nected to the inner shield, the control knob had to 
be provided with a shield insulated from the shaft 
but connected to the outer shield of the condenser 
by a spring contactor. With the condenser thus 
shielded, the capacity Ca ih>195 mii and Cb is only 
5 g/xf- 

The L tk N decade condenser has three terminals, 
.so that it is possible to ground its case to prevent 
hand-capacity troubles. The high terminal of the 
condenser, since it has the smaller capacity to the 
grounded case, is connected to the unknown. With 
this condenser in parallel with the shielded GR con- 
den.ser in the bridge, the effective shunt capacity 


To compensate for wiring resistance, Rt and are 
adjusted for balance with the terminals “series con- 
den.ser’’ and “unknown” shorted, the condensers 
Ca and Co shorted, and R set at zero. The series 
resistance of the condensers can be offset only by 
adjuring the trimmers when an inductance having 
a known value of resistance is connected to the 
“unknown” terminals. Since the accurate determi¬ 
nation of the resistance of an inductor is difficult, 
compensation for the conden.ser resistance cannot be 
achieved with any accuracy. With the bridge con¬ 
nected for the measurement of capacitive unknowns 
a partial compensation is po.ssible, because the trim¬ 
mers can be adjusted with C equal to Cs, the “un¬ 
known” terminals shorted, and R set at zero. Of 




Figure 15. Shielding of variable condenser. 


across the entire arm C..i has lieen found by measure¬ 
ment to be 297 /j/xf, whereas the effective shunt 
capacity across the unknown Cb is 38 iinf. The 297 
nfxi capacity is compensated liy Ct, but the 38 /x^f 
capacity appears as part of the unknown. Except for 
unknowns of high impedance, this small capacity is 
negligible; it is the equivalent of only a few inches of 
shielded cable added to a transducer. 

The proper adjustment of Ct to compensate for 
the capacity Ca is made by adjusting Ct for a 
minimum reading of the detector when the terminals 
“series condenser” and “unknown” (Figure 12) are 
open and the decade and air condensers Co and Ca 
are set at their lowest values. The capacity trimmers 
in the ratio box may be used as a fine adjustment of 
Ct, and the resistance trimmer in this box must be 
u.sed to obtain a sharp balance. If the range of this 
resistance trimmer is not sufficient to obtain balance, 
it may be nece.s,sary to shunt Ct with a resistor to 
compensate for conductance shunting of Ca- 

The series resistance trimmers Rt and R'r are in¬ 
cluded to permit compensation of wiring resistance 
and the equivalent series resistance of the condensers. 


course, the compcn.sation is made only for C set at a 
value equal to Cs’, the variations in the series re¬ 
sistance with a change in C remain uncompensated. 
For many measurements the errors due to the un- 
compemsated equivalent series resistance of the con¬ 
densers are negligible. 

The change from measurement of inductance to 
that of capacitance requires a realignment of the 
bridge. Addition of the capacitor Cs changes the 
value of the trimmer Ct required for balance, since 
the stray capacity from the series condenser Cs to 
ground is added to Ct- The added resistance of Cs 
also requires a readjustment of the resistance trim¬ 
mers for balance. 

The impedance bridge has several major disad¬ 
vantages. 

1. There is a fixed capacity, which cannot be 
offset, shunting the impedance being measured. This 
causes an error in the apparent value of the un¬ 
known that is a function both of frequency and 
of the magnitude of the unknown impedance. The 
mathematical subtraction of this shunt capacity 
is tedious and time-con.suming, especially for the 


CONFIDENTIAL 







250 


MEASUREMENT OF ELECTRICAL CHARACTERISTICS 


L 6 N Ratio Box 



Term'nol 

Box 


L5N Decade 
Capocifor 


L&N Resistance 
Box 


Figure 16. Circuit of admittance bridge. 


series of measurements required to determine an 
impedance locus. 

2. It is impossible to align the bridge accurately 
without the use of an external inductance standard 
for which the equivalent series resistance is ac¬ 
curately known over a wide frequency range. The 
lack of such standards makes the measurement of 
small resistive components with this liridge subject 
to considerable errors. 

3. The change from measurement of inductance 
to measurement of capacitance cannot be made 


rapidly because of the necessity for realigning the 
bridge whenever the change is made. 

4. The measurement of capacitance with this 
form of bridge is inconvenient and often inaccurate, 
because the unknown reactance is balanced by 
the difference between two reactances = 1/wC.s 
— 1/wC. This means that the series condenser C's 
must be chosen so that its reactance at all the fre¬ 
quencies to be measured is greater than the reactance 
of the unknown and, for accuracy, preferably about 
twice the reactance of the unknown. Since the 


CONFIDENTIAL 














































































































IMPEDANCE !MEASURE.MENTS 


251 



Figure 17. Sketcli of admittance bridge console. 


amount of negative reactance occurring in an imped¬ 
ance locus can seldom be predicted, the choice of Cs is 
usually a trial-and-error process, which is time-con¬ 
suming. If a single value of is used for the measure¬ 
ment of a range of reactances, the accuracy of some 
of the measurements may be poor. 

Despite these disadvantages, the impedance bridge 
is very useful in the measurement of impedances ly¬ 
ing within the range in which the effect of the shunt 
capacity in the bridge is negligible and errors due to 
inaccurate resistance alignment are small. Where re¬ 
sults expres.sed as impedance rather than admittance 


or impedance loci rather than admittance loci are 
preferred, the adv'antage of the impedance bridge is 
that the resistance Rx and the series-tuning capacity 
for an inductive unknown are read directly and the 
reactance can be easily calculated. 

The impedance bridge, however, fails in several 
respects to fulfill satisfactorily the requirements es¬ 
tablished for a method of measurement of those 
quantities recpiired to determine the impedance loci 
of transducers. The range of impedances within 
which accurate measurements can be made is insuffi¬ 
cient. The operations required to change the bridge 


CONFIDENTIAL 























































































































2.>2 


MEASUKEMKNT OF ELECTKICAE CHAKACTEKISTICS 



Figure 18. .Vdmittance bridge console and auxiliary apparatus. 


from the measurement of inductance to the measure¬ 
ment of capacitance are time-consuming and involve 
both the use of additional standards and a loss in 
accuracy. The measurement of capacitance with this 
bridge is less convenient and less accurate than that 
of inductance. 

The HCSL Admittance Bridge. Because of the ad¬ 
vantage of a symmetrical bridge network and be¬ 
cause the information obtainable from the vector 
admittance locus is as useful as that obtainable from 
the impedance locus, an admittance bridge of the 
form shown in Figure 5 was also constructed at 
IIUSL. The complete circuit diagram of the bridge 
is shown in Figure 16, a sketch of the bridge con.sole 
showing the arrangement of components in Figure 


17, and a i)hotograph of the bridge con.sole and 
acce.ssory apparatus in Figure 18. 

As in the impedance liridge, a Leeds A Northrup, 
C'ampbell-Shackelton .shielded ratio box (No. 1553) 
.supplies the 1,000-ohm ratio arms, the double- 
shielded input tran.sformer, and the capacitance (Cap 
and B) and conductance (C) trimmers. The variable 
resistance R is an LAN six-dial shielded resistance 
box (No. 4764) with a range of 11,111.1 ohms in 
C.01-ohm steps. The variable capacitance C is com¬ 
posed of the parallel capacitors Co, an LAN three- 
dial .shielded mica capacitor (No. 1071) with a range 
of 1.11 ;uf in O.OOl-juf steps and C..i, and LAN ad¬ 
justable air capacitor (No. 1188) with a range of 50 
to 1,300 mmI (i^ee Figure 16). 


CONFIDENTIAL 






IMPEDANCE MEASUREMENTS 


233 


A blocking condenser Cb has been connected in 
series with the unknown impedance to permit the use 
of superposed direct current to polarize the trans¬ 
ducer without passing this current through any of 
the other branches of the bridge network. To pre¬ 
serve the symmetry of the network, an identical 
condenser has been placed in the opposite arm. These 
two condensers, Cb, are OR Type 509 standard con¬ 
densers each having a calibrated capacitance of 
0.9991 Mf- Since one terminal of these condensers is 
connected to the case of the condenser, this terminal 
has been connected to the corner of the bridge rather 
than to the unknown so that the capacity from 
the case to ground would fall across the whole arm 
of the bridge. If the two condensers are similarly 
mounted, their capacities to ground should balance 
each other. 

In order to change from the measurement of in¬ 
ductance to that of capacitance, the capacitance C 
of Figure 5 must be switched from one arm to the 
other. The operation is performed by two rotary- 
action three-pole, double-throw switches with a 
center off position, Swn and Swa, one for each of the 
condensers Co and Ca- These switches are GR Tyjie 
339-A four-pole, double-throw switches, with one 
l)ole unused. One pole of each switch is used to shift 
the high side of its condenser to either arm of the 
bridge or, in the center position of the switch, to dis¬ 
connect the condenser. Thus the condensers can be 
used in any combination in either arm of the bridge. 

Compensation for residual capacities in the vari¬ 
able resistor and capacitors and wiring capacities 
must be made by equal capacities in the opposite 
arm of the bridge to maintain symmetry and keep 
the bridge direct reading. The residual capacities of 
the condensers Ca and Co are balanced by the 
trimmer condensers Cto, C'to, Cta, and C'ta- Differ¬ 
ences in wiring capacities cause the residuals of Ca or 
Co to vary as the condenser is switched from one arm 
to the other; for this reason a separate capacity trim¬ 
mer is provided for each position of both condensers. 
Two poles of each of the switches are used to connect 
the jjroper trimmer to the opposite arm of the bridge 
as the connections of the condensers are changed. 
Because the residual of the L tk N decade capacitor 
(Co) with the case connected to the low terminal is 
of the order of 70 nfif, the trimmers Cto and C'to nre 
Centralab ceramic trimmer condensers (823AN) with 
a range of 20 to 125 ixfif. Since the L & N air capacitor 
has two terminals rather than three like the L ck N 
decade, its calibration includes the residual, so that 


only the wiring capacity needs be counterbalanced. 
Because this wiring capacity is smaller than the 7 to 
45 mmI range of the Erie ceramic trimmer condensers 
(TS2B) used for Cta aiid C'taj a 20-MMf fixed ceramic 
condenser has been connected in parallel with Ca to 
bring its residual within the range of the trimmers. 

The l)locking condensers Cb, the switches, the trim¬ 
mers, and the associated wiring are mounted on a 
metal panel and shielded by an aluminum case. 
The panel also provides the terminals for the con¬ 
nection of the unknown, the ratio box, and the 
variable resistor and capacitors. This terminal box is 
shown in Figure 19. The blocking condensers and the 



Figure 19. Interior of terminal box for admittance 

liridge. 

trimmer condensers are in.sulated from the panel by 
being mounted on jtolystyrene. The terminals are 
{lolystyrene insulated, GR Type 138-UL liinding 
posts, which afford a very high leakage resistance. 
An extra terminal is provided on the panel above 
the resistance box to permit the insertion of a fixed 
resistor in .series with the variable resistor to extend 
its range. If no series resistor is used, the terminals 
marked Series R in Figure 16 are connected. 

The adjustment of the trimmers to align the 
bridge is made as follows. The high terminal of 
resistor H is disconnected. This is conveniently done 
by removing the short from the two terminals pro¬ 
vided for a series resistor. With the switches Swo 
and Swa in the center position and with the “un¬ 
known” terminals open, the bridge is then aligned 
by adjusting the trimmers G, Cap, and S in the ratio 
box for a minimum detector reading. 

With the decade capacitor Co set at 0.000, the 
switch Swo is thrown first to one side and then the 
other, and the corresponding trimmers Cto and C'td 
are adjusted for a minimum detector reading. With 
Co .set at 0.001 and Ca set at 1,000 nfii, the 
switches Swa and Swo are thrown to connect Ca and 


C'ONFIDENTIAL 









MEASUREMENT OF ELECTRICAL CHARACTERISTICS 


251 


Cd to opposite arms of the bridge. One of the trim¬ 
mers Cta and C'r.i is then adjusted fora minimum 
detector reading. The positions of Ca and Cd are next 
reversed by means of the switches and the other 
trimmer is adjusted. The adjustments of these trim¬ 
mers are made by means of a screwdriver through 
the top of the terminal box. This alignment should 
be practically independent of frequency. 

The reconnection of the resistor H makes the bridge 
ready for use. However, the connection of the re¬ 
sistance box introduces across the arm of the bridge 
a small reactance, which varies in magnitude and 
sign with the setting of the dials. With the box .set 
at 10,000 ohms, the resistance is shunted by a 
capacity of about 10 nfj-f. This introduces a small 
susceiJtance error into the bridge, but for measure¬ 
ments in which the sum of Cd and Ca amounts to 
more than 1,000 /x/jf, this error is negligible. 

For measurements involving smaller capacities, an 
additional alignment procedure is u.sed. With the 
bridge aligned as just described, the resistance box 
is connected and .set at 10,000 ohms and a 10,000- 
ohm L ct N secondary standard a-c resistor (No. 
4640) is connected to the “unknown” terminals. 
The condenser Cd set at 0.001 /xf is connected across 
one arm of the bridge and the condenser Ca set at 
1,000 fiixf across the opposite arm. The bridge is then 
aligned by adjustment of the trimmers in the ratio 
box. This alignment compensates the reactance of 
the resistance box at the 10,000-ohm setting, but does 
not compen.sate for changes in that reactance as R 
is varied. The impedance to be measured is connected 
in parallel with the 10,000-ohm standard resistor. 
For the measurement of inductance-tuning with a 
small capacity, Cd is connected across the unknown 
and Ca acro.ss the opposite arm, while for the mea.s- 
urement of small capacities, Ca is connected across 
the unknown and Cd opposite. If R is disconnected 
or aligned at 10,000 ohms as above, small capacities 
with low dissipation can be readily compared to the 
air capacitor C^ by a substitution method. 

For the measurement of impedances having an 
equivalent parallel resistance above the 11,111.1- 
ohm range of the resistance box R, (that is, admit¬ 
tances having a conductance G less than 0.09 
millimho) the 10,000-ohm standard resistor is again 
used to shunt the unknown. It is easy to subtract the 
0.1-millimho conductance of this standard resistor 
from the measured conductance to obtain that of the 
unknown. The bridge is aligned with this resistor 
and the resistance box connected as before, with 


the capacitors either disconnected by the switches 
being in the center position or connected to opposite 
arms, depending on the magnitude of the capaci¬ 
ties used. 

Although a fixed resistor in series with the resist¬ 
ance box can be used to extend its range, this method 
is not recommended because it may alter the sym¬ 
metry of the bridge and introduce unbalanced re¬ 
siduals, necessitating a large number of calibrated 
fixed resistors to cover the added range. Moreover, 
the adjustment of the resistance is not convenient 
when the resistance box covers only a jiortion of the 
total resistance of R. With a 10,000-ohm shunt re¬ 
sistor acro.ss the unknown, parallel resistance up to 
1 megohm can be measured conveniently and with 
errors within 1 or 2 per cent. 

The advantages of this admittance bridge are: 

1. The bridge can be accurately aligned without 
the use of external standards. This alignment is in¬ 
dependent of frequency and of the magnitude of the 
unknown. 

2. The accuracy of the bridge is limited only by 
the accuracy of the variable resistance and capaci¬ 
tance employed. Within the range of the resistor and 
the capacitors used in the bridge, errors in measure¬ 
ments are less than 0.1 per cent up to at least 50 kc. 
With the range of the resistor extended by shunting 
the unknown with 10,000 ohms, the errors may rise 
to 1 or 2 per cent. 

3. The change from the measurement of induct¬ 
ance to that of capacitance is made very simple by 
means of the switches Sivd and Swa. No realignment 
of the bridge is necessary when the change is made, 
no additional standards are required, and there is no 
lo.ss in accuracy. The calculation of susceptance from 
the reading of the bridge capacitors is the .same for 
both while the sign of the calculated susceptance is 
determined by the position of the switches. 

4. The effect of an impedance, such as that of a 
cal)le or other connecting wires, .shunting the un¬ 
known can be readily eliminated from the reading 
of the bridge. This can be done by aligning the bridge 
with the shunting imj^edance but not the unknown 
connected to the bridge; when the unknown is con¬ 
nected, the bridge reads directly its parallel equiva¬ 
lents. Alignment of the bridge to balance out the 
shunting impedance need be made at only one fre¬ 
quency and can usually be made by means of the 
trimmers in the ratio box alone. 

5. The fact that the unknown and all the variable 
components in the bridge have one terminal grounded 


CONFIDENTIAL 



IMPEDANCE MEASUREMENTS 


255 


considerably simplifies the shielding of the com¬ 
ponents and the control of residuals. 

This admittance bridge .satisfactorily fulfills the 
requirements previously listed for a method of mea.s- 
uring those quantities needed to determine the admit¬ 
tance or impedance loci of tran.sducers. It has, how¬ 
ever, the one di.sadvantage that when an impedance 
locus is preferred or .series equivalents rather than 
parallel equivalents are desired additional computa¬ 
tions are required to convert from admittance to 
impedance. Since the concept of impedance is more 
familiar, although not more useful, than that of ad¬ 
mittance, conversion of the admittance to impedance 
data is required far more often than is conversion in 
the opposite .sense. 

Bridges Developed at BTL. Subsequent to the con¬ 
struction of the admittance bridge, it was found that 
a bridge that satisfies many of the requirements indi¬ 
cated in preceding sections had been developed at 
the Bell Telephone Laboratories. This is the \V-10125 
impedance bridge covering the carrier-frequency 
range from 200 to 150,000 cycles and the impedance 
range of 1 ^h to 100 h and 0.01 ohm to 10 megohms 
with an accuracy of the order of 0.25 per cent. The 
bridge will allow potentials up to 100 volts and cur¬ 
rents up to 0.2 amp to be applied to the impedance 
being measured. 

For the measurement of inductance, this bridge 
takes the form of a Maxwell bridge, shown in Figure 
20, in which inductance is mea.sured in terms of a 
capacitance standard. This is a product-arm bridge 
and hence lacks the advantages of a symmetrical 
ratio bridge. The shielding problem is more complex, 
since the standards are operated off ground. How¬ 
ever, it has the advantage that it can be made direct- 
reading in both inductance and series resistance, since 
the conditions of balance are independent of fre¬ 
quency. The variable resistor R is a conductance 
decade with its resistors connected in parallel and 
calibrated directly in equivalent series resistance. 
This type of decade has the further advantage that 
its capacitance stays relatively constant as the con¬ 
ductance is varied. For the measurement of capaci¬ 
tance, the bridge is changed to the .same form of 
ratio bridge u.sed in the admittance bridge (Figure 5). 
In both forms the resistors r are varied to change the 
range of the bridge. 

Since the determination of impedance loci requires 
the measurement of reactance, the use of a bridge 
that is direct-reading in inductance has no particular 
advantage. A .symmetrical bridge, with all its at¬ 


tendant advantages, can better be used in such 
measurements for inductances as well as capacitors. 
However, the Bell Laboratories’ bridge does suggest 
that the admittance bridge might be improved by the 
incorporation of a conductance decade rather than a 
resistance decade.’^' A decade calibrated directly 
in conductance would eliminate the nece.ssity for cal¬ 
culating conductance from the reading of a resistance 
decade. The conductance decade might also be more 
readily compensated .so that its residual reactance 
does not change with setting. 



At balance: L = r, ^ 

Rz= •'i ^2^ = '■i *“2^ 

Figure 20. Maxwell bridge. 

Auxiliary Equipment 

1. Oscillators. The o.scillators used in connection 
with the impedance and admittance bridges have 
been the GR Type 713-B beat-frequency oscillator 
shown in Figure 18 and the Western Electric 17B 
oscillator .shown in Figure 14. Occasionally a 
Hewlett-Packard Model 205-A special oscillator has 
been u.sed to .supplement the GR oscillator. 

The GR oscillator is very satisfactory for imped¬ 
ance measurements so far as stability and harmonic 
content of the output are concerned, but its dial 
frequency range and scale are not well adapted to 
this work. For mea.surements above 40 kc another 
oscillator or a frequency doubler must be used. For 


CONFIDENTIAL 







256 


MEASUREMENT OF ELECTRICAL CHARAfTERISlICS 


the accurate determination of frequency the oscil¬ 
lator output must be compared to a frequency stand¬ 
ard. An extra frequency control has been added to 
the GR oscillator shown in Figure 18 in the form of 
another variable condenser in parallel with the “cy¬ 
cles increment” condenser and located to the right of 
that condenser. This control was added to permit use 
of the wide frequency spread at the lower end of the 
dial (0 to 1,000 or 20 kc to 21 kc) at other frequencies 



2400 


2000 



-10 -8 -6 -4 -2 0 

GRID VOLTS 


Figure 21. Chanvcteri.stic curve of a 6SK7. 


by setting 17 kc, 18 kc, 19 kc, 20 kc, etc. at the 
21-kc point on the main dial. When an adequate 
frequency standard is employed, there is little need 
for this extra control. The input to the bridge trans¬ 
former is usually connected to the 50-ohm output 
terminals of the oscillator, and the output voltage is 
set at approximately 1.5 volts. 

The WE 17B oscillator has an adequate frequency 
range and scale calibration for use with these 
bridges. However, the oscillator shown in Figure 14 
proved less stable than the GR oscillator. It shows a 
random frequency variation of a few cycles, which 
interfered with a sharp balance. The bridge tran.s- 
foi'mer is connected to the 135-ohm outj^ut of this 
oscillator, and the output is usually set at about 
3 volts. 

The Hewlett-Packard Model 205-A Special has 


good stability and frequency range but is difficult to 
use where small increments of frequency are re¬ 
quired, since its increment control effects a percent¬ 
age deviation in frequency rather than a fixed num¬ 
ber of cycles deviation. It proved useful, however, 
for measurements where the frecpiency increments 
were not less than 500 cycles. 

2. Frequency Doubler. In order to extend the fre¬ 
quency range of the GR 713-B oscillator, a device 
with an output of twice the frequency of its input 
over a range of input frequencies was built. Its oper¬ 
ation requires a circuit having the nonlinear char¬ 
acteristic to be described. If sinusoidal voltage e = E 
cos wf is aj^plied to a circuit having the parabolic 
voltage-current characteristic 


then 


i = Ae Be~, 

i — AE cos utl -|- BE- cos- wf. 


which can be expressed as 


. 

i — \- Ah cos (jit 


BE- 

2 


cos 2(ot. 


The current thus contains components of both the 
input frequency and double that frecpiency. If an¬ 
other voltage e' = —E cos wf = E cos (wf -|- tt), 
which is i)hase-inverted with respect to e, is ajjplied 
to a circuit with the same characteristics, the cur¬ 
rent is 

i' = AE cos {(ot tt) -|- R£"- cos'- (oil -1- tt) 
or 

, BE- , BFA 

t = - AE cos (Jit H-cos 2(jit. 

2 2 

Thus, by adding the two currents, 

i -b i' = BE- -f BE- cos 2cof, 

the term containing the input frequency is elimi¬ 
nated, leaving only a d-c component and the second 
harmonic component. 

The desired parabolic characteristic can be closely 
approximated liy vacuum tubes. By a proper choice 
of operating conditions, the ip vs Cg characteristic 
can be made parabolic over a range of values of 
This is equivalent to a linear vs Cg characteristic. 
The characteristic curve of a 6SK7 is shown in 
Figure 21. Triodes can also be made to have the 
desired characteristic,^'* as shown in Figure 22. The 
elimination of the input frequency from the output 
is achieved by using two tubes with a common load 
but with a push-pull input, as in Figure 23. By using 


CONFIDENTIAL 


































IMPEDANCE MEASUREMENTS 


closely matched tubes, the component of the input 
frecpiency in the output can be made very small. 

The circuit of Fig:ure 24 shows a frequency doubler 
and power amplifier of the type constructed to extend 
the range of the GR oscillator. The input range was 
20 to 40 kc, corresponding to an output of 40 to 80 kc, 
with a constant input voltage of about 1.5 volts. The 
power amplifier was designed to work into a bridge 
input transformer. A 6SC7 double triode operated as 
shown with a 300-volt j^late supply and a fixed bias 
of about 6.8 volts was used as the nonlinear element. 



GRID VOLTAGE Eg 


Figure 22. Characteristic curve of 6SC7. 

The circuit coidd be balanced so that the input fre¬ 
quency component in the output was about 45 db 
below the second harmonic. This is not sufficient for 
good bridge balance but it is usable. The harmonic, 
content of the output could be improved by the u.se 
of octave filters or, if another tuning control be toler¬ 
ated, by a tuned filter. The frequency range could be 
extended by the elimination of transformers. De¬ 
velopment work, however, is impeded by the lack of 
harmonic analyzers for this range of frequencies. 

3. Frequency Standards. The determination of im- 
l)edance and admittance loci requires that measure¬ 
ments be made at a number of accurately known 
frequencies over the range from 1 kc to 100 kc. Be- 
cau.se of the rapid variation in impedance with a 
change in frequency in the neighborhood of leso- 


nance, measurements in this region must be made 
at frequencies that differ by very small amounts. The 
need for frequency increments as small as 10 cycles 
in the region around 20 kc is not uncommon (Fig¬ 
ure 2). This requires an oscillator with wide fre- 
cpiency range and, at the .same time, stability and 
calibration such that small and accurate increments 
of frequency can be obtained within that range. 

Although an oscillator is available that almost sat¬ 
isfies these requirements,®’ one with the range and 
stability but without such an accurate .scale can be 
employed if a suitable standard of frequency is used 



Figure 23. Basic circuit of frequency douiiler. 

to check the output of the oscillator. The frequency 
of the standard is compared with that of the oscil¬ 
lator by use of Lissajous figures on a cathode-ray 
oscilloscope. If a low-frequency .standard is em¬ 
ployed, a large number of frequencies in the oscillator 
range can be checked by the use of the Lissajous 
figures. The ratio of frequencies corresponding to a 
particular Lissajous figure need not be identified, 
since the calibration of the o.scillator should indicate 
which multiple of the standard is being checked. The 
spacing between the frequencies which can be 
checked against the standard should be such that a 
dial on the o.scillator can be used to interpolate any 
desired frequency within that interval. 

Because of its convenience and availability, a 
standard frequency of 1 kc has been used. The 
standard was deri\'ed from a General Radio primary 
frequency standard Cla.ss C-21-HLD located in the 
Cruft Laboratory, Harvard University, and carried 
to the location of the imi^edance measurements on 
telephone lines. This standard alone has been ade¬ 
quate for use with a WE 17B oscillator, which has a 


“ The Western Electric 17B oscillator covers the frequency 
range from 50 c to 150 kc with a scale calibrated every 100 c 
and an accuracy of 25 c at any scale setting. 

^ Such as the Hewlett-Packard Model 205-A Special or the 
General Electric Type 713-B, although the latter ha.s a 
maximum of 40 kc. 


CONFIDENTIAL 

























































258 


MEASUREMENT OF ELECTRICAL CHARACTERISTICS 


lij 



UTC LS-55 



Figure 24. Frequency doubler and power amplifier. 


I Kc 

STANDARD 

FREQUENCY 



Figure 25. Block diagram of multiplier. 


dial scale that can be used for intei’iiolatiou between 
the multiples of 1 kc to the nearest 100 c. For the 
measurement of smaller increments, a GR Type 
713-B oscillator has been used and additional stand¬ 
ard frequencies have been necessary. 

Since the incremental frequency dial on this os¬ 
cillator covers 100 cycles, the interval between the 
frecpiencies that can be checked against a standard 
should be 100 cycles or less. The 1-kc standard pro¬ 
vides a frequency check every 500 cycles; to provide 
other check points within these 500-cycle intervals, 
twelve multiples of the 1-kc standard hav'e been em¬ 
ployed, namely, 7, 8, 9, 10, 11, 12, 13, 17, 19, 23, 29, 
and 31 kc. The Lissajous figures that can be obtained 
with these twelve multiples can be used to cover the 
frequency range between 15 and 40 kc with sufficient 
accuracy of interpolation, although patterns cor¬ 
responding to frequency ratios as .small as 31/23 are 
employed. The existence of a pattern and an idea of 
its complexity, together with the calibration of the 
main oscillator dial, are sufficient to identify the fre¬ 


quency. A table of frequencies that produce usable 
Lis.sajous figures with these twelve standard fre- 
ciuencies has been prepared. 

The twelve frequencies are derived from the 1-kc 
standard by the use of a frequency multiplier, which 
is illustrated in Figure 25. The 1-kc standard signal is 
converted into sharp pulses containing the harmonics 
of 1 kc. The pulses are easily generated from the 
sinusoidal input liy successive stages of clipping and 
differentiation. A tuned circuit is used to select the 
desired harmonic and this harmonic is then ampli¬ 
fied. 

To obtain good Lissajous figures, the standard fre¬ 
quencies should have a clean sinusoidal wave form. 
This means that the tuned circuit should have a high 
Q in order to pass the frequency of the desired 
harmonic but reject the adjacent harmonics. With a 
Q of 200 at 20 kc the adjacent harmonics, 19 and 21 
kc, will be about 25 db below 20 kc, but inductances 
having a of this magnitude at the desired fre¬ 
quencies are hard to construct. 


CONFIDENTIAL 







































































IMPEDANCE MEASUREMENTS 


239 


The necessary high Q can be obtained from a tuned 
circuit employing a coil of lower Q by the addition 
of a negative resistance to the tuned circuit. Such a 
negative resistance can be produced across the input 
of an amplifier by the use of feedback.*'* -*- '*'* -*^ Since 
the tuned circuit has to be followed by amplification 
in order to obtain sufficient output, this method of 
increasing Q is convenient and economical. The 

z 

_A^WWW\AAA/VN_ 



Figure 26. Negative resistance circuit. 


method of obtaining a negative resistance is shown in 
Figure 26. For conditions shown in the figure, the in¬ 
put impedance is 

E 

EE- AE Z 
^ f- z ~ I - a' 

Thus, if .4 is greater than 1, is negative. Since 
dZin/Zin = (lA 1 — .4, the gain .4 of the amplifier 
must not be close to unity for stability. The gain of 
the amplifier can be made stable by use of negative 
feedback. 

If the feedback impedance Z is a resistance R, then 
/fin = R'/l — A. The tuned circuit of Pdgure 27 has a 





——o 






“ L < 

• ^ > 

R In 





c 



' 0 


Figure 27. Timed circuit with negative resistance. 


Q of r/wL without the feedback; with the addition of 
the resistance /fi„, the Q becomes rRin/{r + Rin/oiL)- 
The Q has been changed by the ratio 

Rin/(r + Rin/o^L). 

The circuit of the complete multiplier is shown in 
Figure 28. The 1,000-cycle input is twice amplified, 
clipped, and differentiated by the stages containing 
the first four tubes to produce the pulses. The.se 
pulses are applied to the parallel-tuned circuit, which 
is followed by a two-stage amplifier and a cathode- 


follower output tube. The two-stage amplifier that 
provides the negative resistance u.ses negative feed¬ 
back and a regulated power supply for stability and 
a fairly low impedance output to avoid trouble with 
wiring capacities in the feedback controls. The cath¬ 
ode-follower output stage provides a low impedance 
output and isolates the amplifier stages from the load. 
The tuned circuits, switches, trimmers, and feedback 
adjustments are housed in a separate bo.x for both 
electric and thermal Isolation. For stable operation, 
considerable care must be taken in the arrangement 
of components and wiring. 

The coils u.sed are Western Electric toroids wound 
on molybdenum-Permalloy cores {n' = 125). Higher 
Q'i^ could probably have been obtained at the desired 
frecpiencies by using cores of lower permeability 
{fi' = 26). Three inductances are u.sed to keep the 
capacity required to tune the coils to the 12 fre- 
cpiencies within a convenient range. A pushbutton 
switch selects the inductance, capacitance, and feed¬ 
back required for the frequency desired. The use of a 
pushbutton instead of a rotary switch permits the 
.selection of frequencies in any order without the 
nece.ssity for switching through intervening posi¬ 
tions. A door on the front panel gives ready access 
to the trimmer condenser and feedback adjustments 
for each frequency. These adjustments do not have 
to be made frequently. The pushbutton switch on 
the input circuit jiermits a momentary disconnection 
of the 1,000-cycle input to determine whether the 
feedback circuit is causing oscillation. 

The output of this multiplier is satisfactorily .stable 
at a level of about 10 volts and frequencies of 7, 8, 9, 
10, 11, 12, 13, 17, 19, 23, 29, and 31 kc with a 1-kc 
input of about 5 volts. The selectivity of the tuned 
circuit is .sufficient at any of these frequencies to 
attenuate the adjacent harmonics at least 26 db so 
that the output is more than sati.sfactory for the 
production of Lissajous figures. The effective Q's of 
the tuned circuits range from 100 to 400; they are 
greater for the higher frequencies because of the need 
for greater selectivity at high frecpiencies of resonance 
in order to attenuate a frequency 1 kc off resonance. 

4. Frequency-Comparison Oscilloscopes. The fre¬ 
quency of the o.scillator output is compared with a 
standard frequency by means of the Li.ssajous figure 
on the screen of a cathode-ray tube, to the deflection 
plates of which are applied signal voltages of the two 
frequencies. An oscillo.scope for this purpose requires 
only the cathode-ray tube, amplifiers to supply 
.sufficient voltage to the deflection plates, and a power 


CONFIDENTIAL 

























26<> 


MEASUREMENT OF ELECITRIUAL CHARACTERISTICS 



L W. E. toroids No. Induct. Freq. kc 

D 122802 50 mh 19,23,29,31 

D 127008 145 11,12,13,17 

D 127007 340 7,8,9,10. 

R Selected for proper feedback approximately 20,000 

Figure 28. Frequency multiplier. 


Two such oscilloscopes have been constructed 
for u.se with the impedance and admittance bridges. 

The oscilloscope shown with the impedance bridge 
in hlgure 14, just below the WE o.'^cillator in the 
right-hand rack, contains a single 2-in. 2AP1 cathode- 
ray tube. The upper row of knobs controls the focus, 
inten.sity, vertical and horizontal centering. The 
lower three knobs are gain controls for the oscillator 
and 1-kc and 10-kc injiuts. Two toggle switches per¬ 
mit the horizontal deflection amplifier to be con¬ 
nected to either the 1-kc or 10-kc input and the 
vertical deflection amplifier to be connected to either 
the 10-kc or the oscillator input. Thus the o.scillator 
output can be compared to either the 1-kc or 10-kc 
standard, and the 10-kc output of the frequency 
multiplier can be checked against the standard 1 kc. 
The o.scilloscope input, together with the bridge in¬ 
put, is connected across the 135-ohm output of the 
WE o.scillator. 

The o.scilloscope .shown with the admittance bridge 
in Figure 18, just above the CIR oscillator in the 


right-hand rack, contains two 2-in. 2AP1 cathode- 
ray tubes. The o.scillator output is applied to the 
vertical deflection plates of both tubes, but the 1-kc 
standard is applied to the horizontal plates of one 
tube, while the output of the freciuency multiplier is 
applied to the horizontal plates of the other. This 
permits a continuous compari.son with the 1-kc stand¬ 
ard and a simultaneous comparison with one of the 
standard frequencies from the multiplier. The three 
knobs on the panel are gain controls for the o.scillator, 
1-kc and multiplier inputs. The inten.sity, focus, and 
centering controls for the cathode-ray tubes are 
located behind the panel. The oscillator input to the 
o.scilloscope is connected to the 5,000-ohm output 
terminals of the GR oscillator. 

5. Detectors. Because of the frequency range over 
which the bridge must ojierate and the occasion for 
continuous operation over long periods, an aural in¬ 
dication of balance such as that used in a telephone 
is not practical, and a pointer indicator is preferable. 
A simple form of visual detector is, of course, the a-c 


COXFIDEXTIAL 
















































































































IMPEDANCE MEASUREMENTS 


261 



I «ion«$ 
Plu9 





Ronge 


L « 

WE 0I228II 

ToroTdol Coili— Series Connected — 

1.6 - 2.5 kc C 

Hewittt ~Pocitard 6’6ong Variable Cond. 

L2 = 

” 0122809 


2.4 - 6.5 kc 

125 -4400 ppf 

L3 = 

" 0122804 

.. 

6,4 - 15 


L4 * 

" 0122801 

.. 

14 - 53 


L5 = 

" 0122800 

— Porollel Connected 
Turns Removed. 

45 - 160 




Figure 29. Tuned amplifier bridge detector. 



voltmeter. A voltmeter can be made to ojjerate over 
the required frequency ran^e and, by the use of 
vacuum-tube amplifiers, can be made very sensitive. 
By varying the gain of the amplifiers, the .sensitivity 
of the voltmeter can be altered, so that the response 
of the indicator to the bridge voltage is effectively 
logarithmic and changes in that voltage are easily 
detected, even though the magnitude of the voltage 
varies over a wide range. 

The u.se of a tuned detector is advantageous. The 
maximum usable sensitivity of a detector is limited 
by the noise level due to harmonics in the o.scillator 
output, tube noi.se in the amplifiers, and pickup in the 
bridge wiring and the unknown. With a tuned de¬ 
tector this noise can be reduced and the signal-to- 
noise ratio considerably im])roved, so that the indi¬ 
cation of the detector is po.sitive and steady, even 
though the sensitivity is high. Very small voltages 
can be detected with a tuned voltmeter, thus making 
jjo.ssible a very sharp balance at the bridge. 

A tuned-amplifier vacuum-tube voltmeter for use 
as a detector with the impedance and admittance 
bridges is shown in the circuit diagram of Figure 29. 
The detector is designed to fit the f)ridge consoles but 
it is made portable so that it can be readily removed 
from the con.sole for use with other bridges and for 
measurements at field stations. The detector is shown 


in position in the bridge consoles in Figures 13, 14, 
17, and 18. Its panel contains the meter, a tuning 
control, a band-changing switch for the tuner, and 
coarse and fine gain controls. The connections of the 
external, voltage-regulated power supply and the 
input are made at the rear of the chassis. 

The detector of Figure 29 u.ses three pentode stages 
of a-c amplification, followed by a parallel-tuned 
circuit acro.ss the input of a fourth stage. This fourth 
stage feeds a shunt-type diode rectifier. (Ine half of 
the 6H6 double-diode is u.sed to balance out the 
current due to contact-potential effect in the rectifier, 
so that there is no d-c output when no signal is ap¬ 
plied to the rectifier. A negative voltage from the 
rectifier is applied to the grid of the 6J5. 

The triode 6J5 forms one lu’anch of the Wheatstone 
bridge network of Figure 30. When no d-c voltage 
from the rectifier is applied to the grid of the triode, 
the bridge arms are so adjusted that the bridge is 
balanced and no current flows through the meter. 
If the triode is further biased by a negative voltage 
on its grid, the l)ridge is unbalanced, and a current 
passes through the meter. When the negative voltage 
on the grid reaches the cutoff ])oint of the tube, the 
current through the meter is a maximum, and further 
increases in the signal have no effect on the meter. 
By choosing the values of the bridge comijonents so 


CONFIDENTIAL 


























































262 


MEASUREMENT OF ELECTRICAL CHARACTERISTICS 


that this inaximuni current through the meter causes 
full-scale deflection, the meter can be protected 
against overloading, regardless of large changes in 
the input signal. This type of meter circuit is very 
useful in detectors, since large and rapid changes in 
signal level occur in the process of balancing the 
bridge. The relation of meter deflection to a-c input 
for this meter circuit and rectifier is shown in Fig¬ 
ure 31. 



The meter actually used in construction of the 
detectors was a Weston Model 862-VU meter, be¬ 
cause it has a large illuminated scale and was avail¬ 
able at the time. The internal copper-oxide rectifier 
is disconnected for this application. With the 350- 
ohm shunt shown in Figure 29, the dam])ing of the 
meter is very .satisfactory for use in the detector. The 
first gain control in the amplifier its a 50,000-ohm 
Daven attenuator Type P-621-S having a 40-db 
range in 2-db steps, with the detent mechanism re¬ 
moved to make its operation easier. This attenuator 
was used because of its positive reliable action. The 
second gain control has three steps, giving attenu¬ 
ations of approximately 0, 32, and 65 db. 

With the detector tuned to 20 kc and set at maxi¬ 
mum gain, the input required for 75 per cent of full- 
scale meter deflection is —106 db vs 1 volt. The 
frequency response without the tuned circuit is flat 


within ± 1 db from 2 to 100 kc. The .sharp balance 
obtainable with this tuned detector is evident from 
the experimental curves .shown in Figure 9B; the 
minimum measurable voltage was over 100 db below 
the signal voltage applied to the bridge. 

The amplifier is tuned by means of the parallel 
inductance and capacitance across the input of the 
fourth amplifier stage. The frequency to which the 
amplifier is tuned can be varied continuously over a 



Figure .31. Relation of meter deflection to a-c input. 

range by means of the variable condenser C whereas 
the tuning range can be changed by a .selector .switch 
that choo.ses one of the five inductances Li to L5. 
One jtosition of the range-selector switch discon¬ 
nects the tuned circuit wide-band operation of the 
detector. The detector is tuned to the frequency of 
the signal applied to the bridge by adjusting the 
tuning controls for a maximum deflection of the 
detector meter when the bridge is not balanced. Al¬ 
though this adjustment must be made whenever the 
frequency is changed, thus lengthening the process 
of measurement, experience has proved that the ad¬ 
vantages of a tuned detector more than offset the 
inconvenience of having to tune it. 

Although this type of detector has been very .satis¬ 
factory, the u.se of a detector with phase selectivity 
would facilitate attainment of balance by discrimi¬ 
nating between the effects of reactance and re.sistance 


CONFIDENTIAL 






































IMPEDANCE MEASUREMENTS 


263 



Figure 32. Block diagram of RTF’s cathode-ray detector. 


bridge adjustments. Phase-selective detectors have 
been considered for u.se with tlie impedance and ad¬ 
mittance bridges, but none has been tried. However, 
the development of the vector impedance locus 
plotter in this laboratory ““ has suggested the applica¬ 
tion of this device as a detector. With slight modifica¬ 
tions, the VILP circuit could be u.sed to plot the 
vector ^’oltage appearing across the detector termi¬ 
nals of the bridge, indicating both phase and magni¬ 
tude. This vector could be plotted on the screen of a 
cathode-ray tube, or two meters could be used to 
indicate the magnitudes of the components of the 
vector voltage. The only adjustment neces.sary would 
be that of a gain control in the amplifiers, since the 
circiut is inherently frecpiency-selective and requires 
no tuning. This gain control might conveniently be 
foot-operated, leaving the operator’s hands free for 
the manipulation of the bridge components. 

Another useful type of phase-sensitive detector is 
that described by Lamson.^'' The balance is imlicated 
by an ellipse on the screen of a cathode-ray tube. 
When the bridge is unbalanced the ellipse has its 
major axis tilted from the horizontal, and the ad¬ 
justment of either bridge control will simultaneously 
change l)oth the tilt and the length of the minor 
axis. By varying the phase of the voltage from the 
oscillator applied to the horizontal sweep of the tube, 
the reactive adjustment of the bridge can be made to 
alter only the tilt and the resistive adjustment only 
the length of the minor axis, so that the detector is 
phase-selective. When the bridge is balanced the 
ellipse becomes a horizontal straight line on the 
screen. 

This type of detector is employed by the Bell Tele¬ 
phone Laboratories in their D-169459 and D-170369 


cathode-ray detectors ■*' for use with their W-10135 
and W-10125 impedance bridges. These detectors use 
a tuned amplifier but employ a selective feedback 
network for tuning instead of the L-C circuit used 
in the detectors designed for the impedance and ad¬ 
mittance bridges. A block diagram of these detectors 
is shown in Figure 32. The detectors differ only in the 
frequency range for which they are designed; 
D-169459 covers the range 20 to 20,000 cycles; 
D-170369, 200 to 200,000 cycles. Provision is made 
for the use when desired of a meter instead of a 
cathode-ray tube. The cathode-ray tube can also be 
used to check freciuency if the horizontal plates are 
switched to a standard frequency instead of to the 
bridge oscillator. Some automatic volume control 
[A\X'] is used to prevent overloading when the 
bridge is off balance. 

The use of selective feedback for tuning could 
provide better selectivity than that used in the de¬ 
tector of Figure 22, but sharper tuning does not seem 
to be neces.sary, hence the more exact adjustment 
required is an unnecessary complication. Whether the 
additional adjustment of the jihase-shifting network 
recjuired for phase-sensitive detection can be justified 
by the advantages gained thereby has not been de¬ 
termined, since this type of detector was never tried 
with the admittance bridge or im])edance bridge. 

6 . Polarizing Equipment. The direct current some¬ 
times required to polarize magnetostrictive tran.s- 
ducers is supplied by a 168-volt storage battery. This 
battery is divided into 14-volt sections, which can be 
connected in any series or parallel combination by 
means of a plug-and-jack .system. The current drawn 
from this liattery is controlled by the rheostats and 
meters mounted on a panel located beside the bridge. 


CONFIDENTIAL 













































261 


MEASUREMENT OF ELECTRICAL CHARACTERISTICS 


Two such polarizing ])auels are shown mounted in 
the racks to the left of the bridge consoles in Figures 
14 and 18. The d-c circuit containing the battery and 
polarizing panel components as used to jjolarize a 
transducer is shown in Figure 33. 

Since the imj^edance of the source of direct current 
is in j)arallel with the transducer, the choke shown 
in Figure 33 is connected in series with the high side 
of this source to increase the impedance shunting the 
transducer. The effect of this shunt impedance can be 
made negligil.)le by using a choke with an impedance 
great enough compared with that of the transducer. 
However, the choke must also be capalde of carrying 
large direct currents for relatively long periods. The 


aR.PLUG 



chokes shown on the shelves above the polarizing 
panels in the left-hand racks of Figures 14 and 18 
are satisfactory for most mea.surements. These have 
an inductance of about 170 mh and are self-resonant 
at about 40 kc. There is a ])owdered iron core in.side 
the .solenoidal coil, but the effects of saturation are 
negligible even with direct currents over 6 amp. 
When higher current or impedance is required, a 
special choke must be used and may be ixirallel- 
tuned for maximum impedance. 

Since the rotor of the switch used to change meters 
is not insulated, one side of the polarizing circuit is 
grounded to the polarizing panel, but because one 
side of the transducer is generally grounded, this 
causes no trouble. A single meterwith a variable shunt 
could have been used in this circuit instead of the 
five ammeters, Init this would have recpiired more 
complex switching. 

Treatment of Data. Data are obtained from the 
impedance bridge for an inductive unknown in the 


form of a resistance and a caj^acitance, and for a 
capacitive unknown in the form of a resistance and 
two capacitaiu'es. The resistance read from the bridge 
is the series-ecpiivalent resistance recpiired to plot the 
impedance locus. The required reactance, however, 
must be calculated from the value of capacity 
obtained from the bridge by use of the equa¬ 
tions A' = 1 coF for an inductive unknown and 
A" = 1/coCs — 1 wC for a capacitive unknown. The 
data obtained from the bridge and the results of the 
calculations arc conveniently recorded on a data 
sheet of the form .shown in Figure 34. The calculation 
of reactance can be made on a slide rule in the fol¬ 
lowing manner. The value of the frecpiency on the 
C scale is set af)ove 159 on the D scale. With the 
hairline of the indicator .set at the value of the 
capacity on the Cl or CIF .scale, the reactance is 
read under the hairline on the corresj^onding D or 
DF .scale. 

The data obtained from the admittance bridge are 
in the form of a resistance and a capacity for both 
inductive and capaciti^■e unknowns. The resistance 
is the equivalent parallel resistance of the unknown, 
and the recijwocal of this resistance value must be 
computed to determine the conductance. The .su.s- 
ceptance must be calculated from the capacity 
by use of the relation B = coC, where B is positive 
when the capacity is across the .same arm of the 
bridge as the unknown. The data obtained from 
the bridge and from the calculations are conveniently 
recorded on a data sheet of the form shown in Figure 
35. When the unknown is .shunted by a 10,000-ohni 
resistor, the reading of the resistance box is recorded 
as R, but the 0.1-millimho conductance of this re- 
.sistor is mentally .subtracted from the calculated 
reciprocal of R, so that the recorded conductance F 
is that of the unknown. The susceptance can be 
conveniently calculated on a slide rule in the fol¬ 
lowing manner. The hairline on the indicator is .set 
to twice the value of the freciuency on the D scale. 
The capacity value of the CIF scale is set under the 
hairline. The susceptance is then read on the D scale 
under the index of the C scale or on the DF scale 
above the index of the CF scale. 

When an impedance locus is to l)e plotted directly 
from the admittance bridge data, the data .sheet of 
Figure 36 is convenient. Admittance data are con¬ 
verted to impedance by use of the relations 


R 


a 

(F + 


and 


A' = 


. B 

(F -t- IF 


('ONFIDENTIAL 


























265 


IMPEDANCE MEASUREMENTS 



Figure 34. Impedance data form. 



Figure 35. Admittance data form. 


CONFIDENTIAL 

















































































266 


MEASl REMENT OE ELE(:TRIC;AE CHARACTERISTICS 



G IN MILLIMHOS 
12 3 4 



Figure 37. Conversion of admittance locus to im¬ 
pedance locus. 


The conversion of an admittance locus to the cor¬ 
responding impedance locus or vice versa can be 
made by a simple semigraphical method.® Admit¬ 
tance has been so defined that the admittance vector 
has the same phase angle as its corresponding imped¬ 
ance vector but a magnitude that is the reciprocal of 


® For a discussion of a graphical method of conversion, see 
reference 11. 


that of the impedance vector. Hence the admittance 
and impedance vectors corresponding to a given 
frequency lie along the .same line through the origin. 
Thus in Figure 37, if a line is drawn from the origin 
through any jioint on the admittance locus, .such as 
A, this line must also contain the point on the im¬ 
pedance locus corresponding to the point A. To locate 
this point along the line through A, the length of the 
vector from the origin to A can be measured with a 
compass in terms of the scale of the (i or B axis. In 
h'igure 37 the magnitude of the admittance vector 
with tip A is 2.67 millimhos. By computing the 
reciprocal of the admittance magnitude thus de¬ 
termined, the magnitude of the imjiedance can be 
found. The impedance corresponding to the admit¬ 
tance of point A is 374 ohms. If then, a length 
equivalent to this impedance measured along the 
scale of the B or X axis is laid out with the compa.ss 
from the origin along the line through A, the point 
B on the impedance locus corresponding to A on the 
admittance locus will lie determined. By repeating 
this process for other points on the admittance locus, 
the corresponding impedance locus can be drawn. 
The scale of the impedance axes can, of course, be 
cho.sen arbitrarily and need not be so simply related 
to that of the admittance axes as is the case in 
Figure 37. 

T A etworks. A null method for the measurement 
of impedance can employ T networks instead of 
bridge networks.'*® However, the T networks are not 
well adajited to the routine measurement of trans¬ 
ducers because their ranges of frequency and imped¬ 
ance are not sufficient at the low end, they cannot 
readily be used to measure capacitance, and their 
operation is difficult. They can be used to advantage 


COXFIDEXTIAL 






























































































IMPEDANCE MEASUREMENTS 


267 


for particular ineasurenients within their range where 
the peculiar characteristics of these networks can be 
utilized for higher accuracy than that obtainable 
with a bridge network. 


Xl Rl 



R,= —J- 

L 

Figure 38. Bridged-T network. 

Bri<lged-T. The bridged-T network shown in Fig¬ 
ure 38 is useful in measuring fairly high inductances 
with superposed direct current. The balance condi¬ 
tions of this network are independent of the imped¬ 
ances of the source and the detector. Hence a bat¬ 
tery can be connected in series with either source or 
detector to .superpose a direct current on the induct¬ 
ance being measured, if the source and detector are 
capable of carrjdng the desired direct current. Usu¬ 
ally the source and detector must be shunted by 
chokes to by-pass the direct current, but the size 
of these chokes is not critical since they do not affect 
the accuracy of measurement. No transformer is re- 
(luired because one terminal of both source and de¬ 
tector can be grounded. One terminal of the variable 
resistance can also be grounded, and one terminal of 
each of the condensers is effectively at ground po¬ 
tential since capacities across the source and detector 
do not affect the mea.sured quantities. 

A practical circuit u.sed for the measurement of 
-the impedance of polarizing chokes is shown in Fig¬ 
ure 39. The chokes CH are used to provide a d-c path 
without passing direct current through the oscillator 
or detector. A decade resistor is used for the resist¬ 
ance R, a decade capacitor for C 2 , and a fixed GR 
standard condenser for Ci. The conden.sers are con¬ 
nected .so that most of their capacity to ground falls 
across the source or detector rather than across R, 
where it would become a source of error. Care must 
be taken to avoid coupling between the choke being 
measured and the other two chokes. Balance is at- 


UNKNOWN 
I-1 



Figure 39. Bridged-T circuit for measurement of 
choke imjiedaiice. 



Figure 40. Parallel-T or twiii-T network. 


tained by varying R and Cn for a minimum reading 
of the detector. The magnitude of Ci must be chosen 
so that the value of C 2 for balance is within the range 
of the decade, but Ci can be varied by plugging in 
different sizes of standard condensers. 

Farallel-T. The parallel-T, or twin-T network, 
shown in Figure 40 is useful for the measurement by 
an accurate substitution method of relatively large 
inductances (150 mh) having a high Q (200). As in 
the bridged T, one terminal of both source and de¬ 
tector can be grounded, but in this network one 
terminal of each of the variable standards and of the 
unknown can also be grounded. The conductance of 
the unknown is measured in terms of a variable 
condenser, so that difficulties with the variation of 
reactive residuals in variable resistance standards, 
are avoided. By use of a substitution method in 
which an initial balance is obtained without the un¬ 
known and a second balance with the unknown 
connected, the accuracy of the measurement of su.s- 


CONFIDENTIAL 
























































26K 


MKASIREMENT OF ELECTRICAL CHARACTERISTICS 


ceptance is limited only l)y the precision of the 
variable standards, while that of the conductance is 
limited only by the accuracy of the fixed and variable 
standards or by the exactness with which the con¬ 
ductance condenser can be calibrated with a known 
conductance. 

This network has been used to check the measure¬ 
ments made on the admittance bridge of the Q of 
some toroidal coils, since these coils had a conduct¬ 
ance beyond the accurate range of the bridge stand¬ 
ards (about 0.2 micromho). Two (5R precision air 
condensers were used for the variable condemsers Ch 
and Cg- The other components were so chosen that 
the initial balance and the balance with the unknown 
connected both fell within the range of the.se con¬ 
densers. Very reliable measurements of susceptance 
have been obtained with this network, but the ac¬ 
curacy of the conductance mea.surements has been 
limited by the lack of conductance standards of 
sufficiently small magnitude. 

9.2.3 Measurement by Deflection 
Methods 

The complete and accurate determination of an 
impedance or admittance locus is often unnece.ssary. 
An indication of the existence, relative size, and 
approximate re.sonant frecpiency of the motional 



Figure 41. Voltmeter-ammeter method for impedance 
measurements. 


circle is in many cases sufficient. It is also useful to 
determine only the maxima, such as the maximum 
resistance or maximum conductance and their asso¬ 
ciated frequencies. For the measurement of these 
quantities the accuracj^ of a null method is not re¬ 
quired, and the use of point-by-point bridge measure¬ 
ments is needlessly time-consuming. A deflection 
method of measuring impedance can be used to ad¬ 
vantage where high accuracy and a wide range of 
impedance and frequency can be sacrificed for a gain 
in speed and ease of operation. Another advantage of 
a deflection method is that the effect on the imped¬ 


ance of changes made in the device being measured, 
such as a change in loading, polarization, and tuning, 
can be ob.served contimiou.sly as these variations are 
being made. 

1. Impedometer. A simple method of obtaining a 
meter deflection proportional to impedance is the 
voltmeter-ammeter method shown in Figure 41. If 
the current is held constant while the frecpiency is 
varied, the voltage F is proportional to the magni¬ 
tude of the impedance Z. The voltmeter can lie 
calilirated to read impedance. 

A form of this circuit employed for impedance 
measurements is shown in Figure 42. This has been 
called an impedometer. A constant current is obtained 
by using a resistance, which is large compared to the 

r»Z 



impedance being measured, in .series with a constant- 
voltage generator. The voltage acro.ss the unknown 
impedance Z is mea.sured with a .sensitive vacuum- 
tube voltmeter, .such as the Ballantine Model 300 
electronic voltmeter. The voltmeter is calibrated to 
read impedance by comparing the deflection pro¬ 
duced by the unkno\Vn to that produced by a known 
impedance, such as the resistor Rs- With the \'olt- 
meter across the known impedance, the current can 
be adjusted to produce a convenient deflection of the 
voltmeter by varying the voltage E. 

The .same circuit can be used to mea.sure impedance 
by a comparison method, if higher accuracy than that 
obtainable by the deflection method is desired. The 
voltmeter is switched alternately to the unknown 
and to a variable standard impedance, such as a 
decade resistor. If the standard is varied until the 
.same deflection of the voltmeter is produced by both 
impedances, the magnitude of the unknown is equal 
to that of the standard. The accuracy of the volt¬ 
meter calibration does not affect this measurement. 

The imt)edometer circuit has been u.seful for rough 
mea.surements of impedance magnitudes. It has also 
found application in determining the relative diam¬ 
eters of motional impedance circles and the approxi¬ 
mate resonant freciuencies. The resonant frequency 


CONFIDENTIAL 





















IMPEDANCE MEASUREMENTS 


269 


can be approximated by finding the average of the 
two frequencies that i;)roduce the minimum and 
maximum impedance in the region of resonance. 
This average frequency is useful as a criterion for the 
comparison of the re.sonant frecpiencies of the trans¬ 
ducer elements in imdtielement transducer produc¬ 
tion. 

2. Admittometer. In a manner similar to that 
used for impedance, a deflection proportional to ad¬ 
mittance can be produced with the circuit of Figure 
43. Since I = EY, if the voltage is held constant the 
current I is proportional to the admittance Y. The 
ammeter I can be calibrated directly in admittance. 



Figure 43. Voltmeter-ammeter method for admittance 
measurements. 


An admittometer circuit is shown in Figure 44. A 
constant voltage generator is u.sed to supply the 
voltage E. The current is measured by a sensitive 
voltmeter connected across a small resistance r in 
series with the unknown. The admittance of r should 
be large compared with that of the unknown. The 
voltmeter is calibrated by connecting a known ad¬ 
mittance, such as a resistor R, in place of the un¬ 
known. 



Figure 44. .Admittometer circuit 


3. Revolving Circuits. In both the impedometer and 
admittometer the meter deflection indicates only the 
magnitude of the vector impedance or admittance. 
The characteristics of the impedance or admittance 
loci could be better determined if the pha.se of the.se 
vectors was also indicated. One method of indicating 
both the phase and magnitude of the vectors is to 


obtain meter deflections proportional to both the 
resistive and reactive components of the impedance 
vector or to the conductive and susceptive com¬ 
ponents of the admittance vector. To produce such 
deflections, voltages proportional to the desired 
components must be obtained from the device being 
mea.sured. 

R 

-vwvwwwv-- 


'8 


__J 

Figure 4.5. Impedometer circuit. 

In the impedometer circuit of Figure 45, with the 
resistance R sufficiently greater than the impedance 
Zq to make the current through Zq independent of 
the changes in Zo and to make that current have the 
same phase as the voltage E, the voltage Fo appearing 
across Zq is proportional in magnitude to Zq and 
differs in phase from the current and hence the volt¬ 
age E by ^ = arc tan Xo/Rq, the phase angle of Zq. 
Similarly in the admittometer circuit of Figure 46, 



Figure 46. Admittometer circuit. 


with the conductance of the resistor R so large com- 
Itared to the admittance of I’o that the current 
through Fo is proportional to To, the voltage To ap¬ 
pearing acro.ss the resistance R is proportional to the 
magnitude of Fq and differs in phase from the voltage 
Ehy 4) = arc tan Bq/Gq, the phase angle of Fq. Hence 
in both circuits there appears a vector voltage Fq 
which is proportional in magnitude to the vector 
impedance or admittance and has a phase angle with 
respect to another voltage E which is the same as 
the phase angle of the impedance or admittance. 



CONFIDENTIAL 








































270 


MEASUREMENT OK ELECTRICAL CHARACTERISTICS 


The two components of I’o, one, | To 1 cos 4>, l^l^ose 
with E and the other, | To | sin </>, in quadrature 
with E, are therefore proportional respectively to 
the real and imaginary components of the vector im¬ 
pedance or admittance. 



The resolution of such a vector voltage To into two 
components, one in phase and the other in quadra¬ 
ture with a voltage E (Figure 47), can be accom¬ 
plished electrically with the following component¬ 
taking or “resolver” circuit (also known as a 
phase-sensitive detector circuit). The switch in Fig¬ 
ure 48 is controlled by the polarity of the voltage E. 

open: e 
closed: E >0 

-1-o- 

SWITCH 



Figure 48. Resolver circuit. 

For example, when E is positive the switch is closed, 
when E is negative the switch is open. The voltage E 
does not appear in the circuit of Figure 48; it merely 
operates the switch. When the frec[uency of E is the 
same as that of T'o but the phase difference is </>, these 
voltages may be expressed as 

Fo = I Fo I smd 

E = \ E \ sin (d — 0), 


and the current i through the circuit is 

i = — = LLuJ ])ositive, switch clo.sed) 

R R 

i = 0 [E negative, switch open). 

The average current through R is (Figure 49 1 


or 



cos 0. 


Hence, the d-c voltage appearing across R is propor¬ 
tional to I Fo I cos 0, which is the desired component 
of Fn in i)hase with E. 


SWITCH 



Figure 49. Phase diagram with E in phase with Fq. 


To obtain the quadrature component, the phase 
of E is shifted 90 degrees, .so that 


E = 


,, I . 0 — 0 — TT 

h sin- 


The average current through R is now (Figure 50) 

-•0 + 3jr/2 

tave = —I I Fo I amddd 


2TrRJ(t> + ir 2 


or 


-I Fo 

ttR 


sin 0. 


The d-c voltage across R is thus proportional to Fo 
sin 0, which is the component of Fo in quadrature 
with E. 


CONFIDENTIAL 





























IM PE I) A N (; K M E A S L K E M EN rs 


271 


Since the switch of Figure 48 must operate at 
switching frequencies up to 100 kc without phase 
error, any mechanical switch is impractical. One 
type of switch that can he used in the resolver circuit 
is an electronic switch in which the plate current of 
a imdtielectrode vacuum tube is cut off by a change 

SWITCH 



in the potential applied to one of the electrodes. The 
switching voltage can be applied to the j)late, to any 
one ol the grids, or to the cathode. With a signal 
voltage apj)lied to the control grid, the tube func¬ 
tions as a normal amplifier of that signal for one 
polarity of the switching potential but cuts off the 
signal for the opposite polarity. This implies that 
the wave form of the switching voltage must be 
square in order to maintain proper electrode poten¬ 
tials during the half-cycle when the tube is to 
function as an amplifier and to cut off the jjlate cur¬ 
rent completely during the other half-cycle. 

Another type of .switch that can be used in this 
resolver circuit is the bia.sed rectifier, illustrated in 
Figure 51. If the rectifier is as.sumed to be ideal and 
the .switching voltage E is greater than F, the cur¬ 
rent through R is a function of 1' for one polarity 
of E and is zero for the opposite polarity. When the 
rectifier conducts, there is, of course, a component 
of current due to the .switching voltage E. This can 
be eliminated from the output by using a balanced 
circuit, as shown in Figure 52. If the a-c switching 
voltage E is large compared with the signal voltage 
r, the cutoff of the rectifiers is sharp and the switch 




Ficcre .51. Hi.'ised rectifier .switch. 


is effectively open for one half-cycle of E. The recti¬ 
fiers can be either varistors or diodes.-'** 

4. Conductonieter. The point of maximum conduct¬ 
ance on the admittance locus of a resonant trans¬ 
ducer is useful as a criterion of both the ijotential 
efficiency and the frecpiency of maximum efficiency 
of the tran.sducer because the principal diameter of 
the motional admittance circle is for many trans¬ 
ducers nearly i)arallel to the conductance axis. The 
determination of the frecpiency and the value of the 
maximum conductance by bridge methods is too 
tedious and time-consuming to be applicable in 



Figure 52. Balanced switch circuit. 


production testing of large numbers of transducer 
elements. A deflection method combining the ad- 
mittometer circuit with a resolving circuit in an 
instrument known as a conductometer is very u.seful 
for such measurements. The conductometer indicates 
on a meter the magnitude of the conductance of a 
transducer as a function of frequency. 


CONFIDENTIAL 












































272 


MEASUREMENT OE ELECTRICAL CHARACTERISTICS 


The circuit of a coiuluctonieter is shown in Figure 
53. This circuit is a combination of the circuits of 
Figures 46 and 52. The source of constant voltage 
required by the admittometer circuit is the feedback 
amplifier shown in Figure 54, which has an output 
impedance of less than 0.1 ohm. Since the resistance 
r, across which the voltage V appears, adds to the 
effective impedance of the source, this resistance 
must be kept small to maintain a constant voltage 

transform ( data 

VARISTOR CORE : 2 mil HYPERSIL 



F'igure 53. Conductometer circuit diagram. 


across the transducer but must also be large enough 
to provide a usable voltage. With a 0.1-ohm resistor 
in series with the source, the total source impedance 
is about 0.2 ohm. In consequence, the amplifier can 
maintain an a-c output voltage constant within 4 per 
cent across a load whose admittance may vary from 
0 to 200 millimhos. 

The resolver circuit uses varistors as the rectifiers. 
The switching voltage is the same voltage from the 
amplifier output that is applied to the conductom¬ 
eter circuit. The signal voltage F is obtained from 
the 0.1-ohm series resistor through a 10-to-l step-up 
transformer. The maximum usable switching voltage 
is limited by the 2-volt maximum allowable voltage 
on the varistors. With an amplifier output voltage 
of 1.5 volts, the conductance of the unknown can 
rise to 200 millimhos before the signal voltage ceases 
to be le.ss than one-tenth of the switching voltage. 


In the circuit shown, with an input voltage of 1.5 
volts a conductance of 100 millimhos producesa40-Ma 
current through the meter. 



windings: 

primary: 1032 TURNS ’'sa ENAMEL,C.T. 

secondary: 10 turns W'xJiz 

COPPER STRIP 

Figure 54. Conductometer amplifier diagram. 

This conductometer is used as follows. An oscil¬ 
lator and power supply are connected to the ampli¬ 
fier. The input to the amplifier should be about 1.5 
volts. With the switch on position 2 (Figure 53), the 
resolver circuit is balanced by adjusting the 50-ohm 
])otentiometer so that the meter reads zero. With 
the switch thrown to position 1, the meter is cali¬ 
brated by adjusting the input voltage, using the 
potentiometer on the amplifier input as a fine adjust¬ 
ment, so that the meter reading corresponds to a 
conductance of 100 millimhos. With the switch 
thrown to position 3, the meter reads the conduct¬ 
ance of the unknown admittance connected to the 
terminals. 

This conductometer circuit cannot be used over a 
wide range of frequencies because of the difficulty in 
maintaining the balance of the resolver circuit, which 
prevents the switching voltage from appearing in the 
output, and becau.se of the difficulty in designing the 
transformer To so that it has no phase shift as a 
function of frequency. However, the conductometer 
circuit was very useful in the j)roduction testing of 
laminated-stack transducer elements. In testing 
HP-3 stacks it was possible to determine easily and 
quickly the frequency of maximum conductance in 
air to within 0.02 per cent and the maximum con¬ 
ductance within 5 per cent. 


CONFIDENTIAL 
























































IMPEDANCE MEASUREMENTS 


273 


5. Vector Impedance Locus Plotter [VILP], The 
use of deflection methods of measuring; a vector 
impedance or admittance can lie extended ultimately 
to the automatic jilotting of the locus of the vector. 
Since a combination of the impedometer or admit- 
tometer circuit and two resolver circuits can provide 
d-c voltages proportional to the two components of 
the ^’ector impedance or admittance, these voltages 
can he used to operate a mechanical plotter or can 
be apjilied to the deflection plates of a cathode-ray 
tube to produce a trace of the locus on the .screen of 
the tube, thus providing a very quick and easy 
method of measuring transducer characteristics. 

A VILP was constructed for this purpose. It traces 
the locus of the tip of an impedance vector 
Z ~ R -\- jX by jilotting A' against R on the face of 
a cathode-ray tnbe as the frecpiency of the applied 
signal is varied. This action is produced by the use 
of the impedometer circuit to provide a voltage V 
(Figure 45) across the imi^edance Z, which is propor¬ 
tional to the magnitude Z and has a phase angle 
with resj)ect to the injnit voltage E equal to the phase 
angle of Z. Two resoh'er circuits are u.sed to obtain 
d-c voltages proportional to the components of F 
that are in phase and in (luadrature with the voltage 
E. These d-c voltages projjortional to the real and 
imaginary comijonents of Z are apiilied to the hori¬ 
zontal and vertical deflection plates of a cathode-ray 
tube. A transparent screen that bears suitable rulings 
is mounted in front of the cathode-ray tube and 
provides the coordinate axes. 

The resolver circuits of the VILP enq^loy an 
electronic switch because it is more suitable than the 
rectifier switch at high frequencies and at the high 
voltage and impedance levels required for cathode- 
ray deflection. As stated in the discu.ssion of resolver 
circuits, the electronic .switch reciuires a square-wave 
switching voltage. To obtain a scpiare wave form 
from a sinusoidal switching voltage, a peak-clipping 
or limiting circuit can be used. The switching tube 
can itself serve to clip one of the peaks by use of the 
cutoff point of the electrode to which the switching 
voltage is applied. Since the rectangularity of the 
wave form increa.ses with the proportion of the peak 
that is clipped, the voltage .swing recpiired on that 
electrode to cut off the tube .should be small, .so that 
a .sati.sfactorily rectangular wave can be obtained 
without the application of an unduly large ampli¬ 
tude sine wave. The amplitude of the sine wave 
applied to the clipper must be sufficient to produce 
a .satisfactorily rectangular wave but must not ex¬ 


ceed the value that will cause distortion of that 
wave in the circuits in which it is generated or in 
those circuits to which it is applied. Within these 
limits, the effect of variations in the amplitude of the 
switching voltage iq^on the rectangvflarity and am])li- 
tude of the stpiare wave, and hence upon the switch¬ 
ing action, will be small. 



Figure .55. Electronic .switch. 

A .sharp cutoff at a relatively low voltage can be 
obtained by applying the switching voltage to the 
cathode of a triode.*’ A second triode (Figure 55), 
which has its catliode connected to that of the 
switching tube, is used to bias the switching tube to 
cutoff and, at the same time, to clip the other peak 
of the .switching voltage. When the voltage E swings 
positive, the increase in cathode current cuts off 
tube B] when E swings negative, tube A is cut off. 
The biases of the two tubes are .so adjusted that the 
output of tube B with no signal Fq is a .symmetrical 
square wave and with tube A cut off tube B is prop¬ 
erly biased to amplify Fq. The voltage at the plate 
of B as a function of time is shown in Figure 56. 



Figure 56. Plate voltage wave forms. 


As Figure 56 shows, the output due to Fq is in the 
form of half-wave pulses, which must be filtered to 
produce an average d-c output proportional to | Fq | 
cos 0. Less filtering is necessary with the full-wave 
circuit of Figure 57 and the d-c output for a given 
input Fo is also doubled. In this circuit both the 
signal and the switching voltage are pha.se-inverted 

The DuMont Type 185-.A electron switch and square- 
wave generator emjiloys a similar method of switching. 


CONFIDENTIAL 


































MEASUREMENT OF ELECTKICAE CMAKACTEKISTICS 


271 



Figure 57. Full-wave switching circuit. 


1 


SUPPLY VOLTAGE 


Epovg 


EpO V( 




fVfv" 


Vo = 0 ^t Vo in Dhose with E 1 Vo 90® from E 1 

Figure 58. Plate voltage wave forms. 



Figure 59. Balanced full-wave switching circuit. 

and fed into two switoliing tnbe.s with a common 
plate load. Since one tube is alway.s conducting while 
the other is cut off, the plate remains at a constant 
potential when no signal To is applied. The plate 
voltage as a function of time is shown in Figure 58. 
A further advantage of this circuit is the fact that the 
permissible d-c plate voltage swing due to the signal 
is doubled, since the average plate ^■oltage with no 
.signal I’o is the operating plate potential of the tube 
(Figure 58) for this circuit, while for the half-wave 
circuit it is the mean value of the plate supply volt¬ 
age and the operating potential (Figure 56). 

For a balanced d-c outinit, two of the circuits of 
Figure 57 can be combined, as shown in Figure 59. 
The output of this resolver can be connected direct!}' 
to the plates of a cathode-ray tube, since the output 


t- 





R, 







fCl 

DIFFERENCER 





AND 


- 1 1 

CM 

o 

- >- •o 

L t 

Uj 

I 

« 1 

L 

AMPLIFIER 

T 

V<9< 

_ L 


Figure 60. 90-degree pha.^e shifter. 



Figure 61. h'requency re.sponse of phase shifter. 


voltage .swing of the re.solver tubes can be made large 
enough for cathode-ray tube deflection. Connection 
of the deflection plates directly to the resolver is not 
convenient because of the difhcidty of adding to the 
resolver circuit a positioning control for the beam of 
the cathode-ray tube. For this rea.son, a cathode- 
coui^led push-pull amplifier stage, directly collided to 
the output of the full-wave, unbalanced-output re¬ 
solver of Figure 57, best serves to provide balanced 
deflection voltages, together with a means of initially 
positioning the spot. 

It was noted above that the .switching voltage E 
must be shifted 90 degrees in phase in order to ob¬ 
tain the sine component of Fo. Therefore a circuit is 
required that will give 90 degrees of phase shift over 
a wide range of frequency. .A. further requirement is 
that the magnitude of the output voltage of this cir¬ 
cuit should be nearly constant with freciuency, since 
changes of more than appro.ximately 6 db in the 
switching voltage cannot be tolerated by the resolver 
circuits. The.se requirements can be met by a circuit 
con.sisting of two con.stant-resistance, all-pass, lattice 
networks whose outputs differ in phase by 90 degrees 
when they are fed from a common source.-^ However, 
the u.sable frequency range is limited to two octaves, 
and the networks are relatively complex,requiring the 


(’OXFIDENTIAL 




































































IMPEDANCE MEASUREMENTS 


275 



Figure 62. Complete block diagram of first vector impedance locus plotter. 


careful adju.stment of numerous components. A much 
simpler circuit (Figure 60) can be made to perform 
the required functions over a wider frequency range 
with very .small phase error and amiilitude variation. 
If co/fiCi > > 1, the voltage Ci in Figure 60 leads F 
by 90 degrees and its amplitude increases linearly 
with frequency, while if > > 1, the voltage Ci 

lags 1' by 90 degrees and its amplitude varies in¬ 
versely with freciuency. As Figure 61 shows, liy taking 
the difference of these two voltages (note that e-i is 
180 degrees out of phase with ei and is therefore 
plotted as a negative voltage), their amplitude vari¬ 
ations can be made to compen.sate each other par- 
tiall}', so that the difference varies le.ss than +2.5 db 
over a decade range of frequency. The minimum 
value of Cl — occurs approximately at the fre¬ 
quency at which coAht'i = 1 The output volt¬ 

age of this circuit can be kejit as nearly in (juadrature 
with the injiut F as desired by the choice of the 
products w/fiFi and oiR 2 (\, with a limit imiiosed by 
the iiermlssible attenuation of the network. 

A complete block diagram of the first VILP is 
shown in Figure 62 and the complete circuit dia¬ 


gram in Figure 65. A cathode-follower stage is placed 
at the signal input to prevent any possible loading of 
the oscillator and to present a low impedance to the 
various circuits of the VILP. A voltmeter is included 
in order that the voltage E upon which the constant 
current depends may be easily adjusted to the correct 
value to preserve the calibration of the instrument. 
The constant-current resistor is variable in eleven 
stejis from 2,000 ohms to 5 megohms, corresponding 
to plotting impedances with maximum values of 
20 to 50,000 ohms respectively. The self-capacity 
of the 5-megohm resistor is sufficient to cause con- 
sideralile phase error and some amplitude error iu 
the constant current at 100 kc. The pha.se-correction 
network in the signal amplifier channel is designed to 
correct this defect. Hence capacities are added in 
parallel with all lower values of constant-current re¬ 
sistors so that their RC time constants are all equal 
and the one phase-correction network will serve for 
all values of the constant-current resistor. Since this 
network is a relatively low-impedance circuit, the 
I)otentiometers controlling the gain in the two 
channels R and X are included here. The check-gain 


CONFIDENTIAL 































































































276 


MKASI KEMENT OF ELECTRICAL CHARACTEKIS I ICS 



Figure 63. First model of VILP. 

ponent switching: voltage is applied to both resolvers, 
and if the 50-ohin resistor is selected, the deflection 
shonld correspond to 50 + joO ohms. (Each channel 
is in this instance taking the same com|)onent of that 
impedance and should show ecpial deflections.) The 
instrument can lie calibrated by adjusting the gain 
controls in each channel to show a deflection of ex¬ 
actly 50 + ./50 ohms when the voltmeter indicates 
the proper value of input signal. The amplitude of 
the switching voltage applied to the cathode fol¬ 
lowers in the if channel is 25 volts and that in the X 
channel has a minimum of 20 volts. Wire-wound re¬ 
sistors (100-ohm are placed in series with 

many of the grids of the phase-shift compensated 
amplifier tubes. This has pro\ ed an effective method 
of preventing parasitic oscillations. Controls on the 
d-c amplifiers allow an initial positioning of the spot 
before an impedance locus is plotted. The transparent 


screen bearing the coordinate axes is movable to 
allow the first and fourth C[uadrants of the impedance 
plane to be centered on the screen. No provision is al¬ 
lowed for jilotting in the second and third cpiadrants. 

The amplifier and pha.se-inverfer stages in the 
signal and switching-voltage channels have been 
compensated for phase shift due to capacity from the 
plate circuit to ground. The proper value of induct¬ 
ance to be placed in series with the plate resistor was 
determined by ob.serving the pha.se shift of the stage 


Figure 64. Photograph of impedance locus on VILP. 

as a variable inductance was adjusted. A ladder 
attenuator having a low characteristic impedance 
was constructed of BT-1 (metallized) resistors and it 
was assumed that this attenuator was free from phase 
defects. The signal from this attenuator was amplified 
by the stage being tested, and the output of the 
stage was compared with the input signal to the 
attenuator on a cathode-ray o.scilloscope. A cathode 
follower was used as a high-input impedance stage to 
take the signal from the plate circuit, since even 
small added capacities affect the pha.se .shift .seri¬ 
ously. It was found neces.sary to have the following 
stage connected and operating before this phase-shift 
correction could be made. When the proper induct¬ 
ance value was determined, coils were wound on small 
Western Electric toroidal cores, making \’ery com¬ 
pact inductors. An amplifier with zero pha.se .shift 
and cathode-follower input and output stages was 
constructed for comparing the phase of the relatively 


switch in the A' component switching t'oltage channel 
allows the R component .switi'hing voltage to be ap¬ 
plied to both channels. The switch at the input to 
the signal amplifier channel allows the .selection of 
zero impedance, 50 ohms, or connection to the 
terminals of the impedance to be plotted. If the 
check-gain switch is thrown so that the R com- 


C(3NFIDENTIAL 
































































l'’i(junK ()i). Vcctoi- iin|)(>(lanc(‘, locnis plottfi' circuit ilia>;riiiu. 


CONFIDENTIAL 


































































































































































































































































































































































1 









IMPEDANCE MEASUREMENTS 


small T"o signal at the input of the resolvers with the 
switching voltage in the same manner. These numer¬ 
ous custom-tailoring phase-shift adjustments made 
the construction of the first VILP a slow proce.ss. 

The first model of the VILP is shown in Figure 63. 
The rack contains the cathode-ray tube chassis, the 
\TLP chassis, and the power supply for the VILP. 
An oscillator, .such as the H-P Model 200-D, is u.sed 
to supply the variable frecpiency voltage to the VILP 
chassis. An example of an impedance locus traced 
on the screen of the cathode-ray tube is shown in 
Figure 64. The impedance locus shown is that of a 
magnetostrictive transducer element in air over a 
freciuency range of 10 to 50 kc. 

The first model of the MLP (Figure 65) still has 
many defects. The upper limit of the impedance it 
can plot is established by the size of the constant- 
current resistors and their shunt capacity. Even the 
5-megohm resistor, which is the highest value now 
u.sed, has phase defects that indicate that it cannot 
be considered as a pure resistance shunted by a 
capacity but as a much more complicated network. 
The phase correction network shoidd, therefore, be 
much more elaborate. Perhaps the development of 
.some sort of vacuum-tube constant-current gener¬ 
ator would serve to eliminate these difficulties and 
allow the plotting of impedances uj) to 1 megohm. 
The output voltages of the resolver tubes are not 
entirely independent of the amplitude of the switch¬ 
ing voltage and .some motion of the spot occurs in the 
A' direction, as the frecpiency is varied even when 
the selector switch is on zero impedance. This is due 
to the change in shape of the square wave as the 
amplitude of the A' switching voltage varies with 
frequency. A bias voltage is applied to the grids of 
the cathode-follower switching tubes by means of a 
battery so that tube A in Figure 55 will cut off at the 
proper point for the production of a good square 
wave. The motion of the spot on the cathode-ray 
tube which is due to changes in the amplitude of the 
switching voltage is critically dependent upon the 
value of this bias ^’oltage. It is hoped that this diffi¬ 
culty can be overcome in .some way. The operation of 
the first two tubes of the signal amplifier channel 
from an a-c filament supply generated so much noise 
that the spot on the cathode-ray tube screen was 
unduly large. A d-c filament supply is, therefore, used 
for the.se two tubes. Perhaps the u.se of a different 
tube with better noise characteristics than the 6AC7 
will allow use of the a-c filament supply for all tubes. 

The VILP could be converted to a vector admittance 


locus plotter [VALP] by using the admittometer cir¬ 
cuit instead of the impedometer circuit to obtain the 
vector voltage F from the device being measured. 
The VALP would eliminate the troubles with phase 
angles of the large resistors recpiired to produce a 
constant current through high impedances in the 
VILP circuit, since the VALP circuit employs a 
constant voltage source and a .small series resistor. 
Use of a series resistor to measure current, however, 
makes it impossible to ground at the same time one 
terminal of the voltage .source, of the impedance 
being measured, and of this .series resistor. The VALP 
would be u.seful in plotting the high impedances that 
cau.se trouble in the VILP circuit, but the VILP is 
more applicable to low impedances. 

The resolving circuits of the VILP can, of course, 
be u.sed to plot the locus of any vector voltage F. One 
such application is the plotting of the transfer imped¬ 
ance of a four-terminal network. This was tried with 
the present VILP circuits with encouraging results. 

The VILP proved very useful in the measurement 
of impedance loci, both as a substitute for, and a 
complement to, the bridges. In many cases the MLP 
trace can supply all the desired information very 
cpiickly. This is particularly true in experimental 
work where an indication of the effect of changes in 
the transducer on the impedance locus is .sufficient. 
The effect of such changes can be observed on the 
VILP screen as the changes are made. This was par¬ 
ticularly u.seful in determining and eliminating the 
effects on impedance loci of refiections in the ab¬ 
sorbent-lined tanks. A preliminary measurement on 
the VILP can .save much time and effort, even when 
bridge measurements are reciuired, by indicating the 
approximate size and complexity of the locus and the 
resonant frequencies and by indicating defects in the 
tran.sducers, such as .short or open circuits, which 
can be remedied before time is wasted on bridge 
measurements. 

9.2. t Loading 

Analysis of transducers by the use of impedance 
loci recpiires that the imjjedance of the transducer be 
measured with the transducer radiating into a water 
load. In addition to the electrical problems mvolved 
in measurements with the transducer under water, 
the problem of obtaining the proper load on the face 
of the transducer is encountered. The radiation im¬ 
pedance into which the transducer is working may 
differ from the ideal radiation load of water because 


CONFIDENTIAL 



278 


i\ieasurp:ment of electkicai. chakactekistics 



of the formation of air bubbles on tlie transducer face 
or the return of energy to the transducer whic'h re¬ 
sults from reflections. 


The |)resence of large quantities of air in the water 
results iu the formation of a layer of minute bubbles 
on the surface of an immersed transducer. Such 


CONFIDENTIAL 





















































IMPEDANCE MEASUREMENTS 


279 


formation is particularly rapid and troublesome if 
the temperature of the transducer is higher than that 
of the water, as is often the case when the transducer 
is polarized with several amperes of direct current. 
The solubility of air in water in contact with the 
heated transducer face is reduced, so that some air 
comes out of .solution and collects on the transducer 
face in the form of small bubbles. The load on the 
tran.sducer then approaches that of air alone. Water 
from the city mains was found to contain a large 
cpiantity of air, so that a tank filled with this water is 
practically useless for inpiedance measurements until 
the dissolved air has been removed. The water wilt 
become .sufficiently air-free after being in the tank 
for a week or more, but heating the water by the use 
of electric immersion heaters or by releasing live 
steam into the tank will speed up the proce.ss. For 
maximum effect the water should be boiled, tnit this 
is difficult with large cpiantities. 

To hasten the wetting of the tran.sducer face, a 
wetting agent such as Aerosol OT. in a 25 per cent 
water .solution is usually applied. Even with the use 
ot a wetting agent, it is sometimes necessary to al¬ 
low the transducer to soak for hours before it is 
thoroughly wet. This is particularly true of lami¬ 
nated stacks without rubber faces, where the con¬ 
solidating material on the face apparently is difficult 
to wet. 

The presence of reflections causes the radiation 
impedance into which the tran.sducer is working to be 
a function both of frequency and transducer position, 
so that the conditions of measurement are not only 
difficult to reproduce but also are not tho.se of open 
water. The changes in radiation impedance due to re¬ 
flections are evident in measurements of the electric 
impedance of the transducer. The magnitude of the 
changes in electric impedance resulting from reflec¬ 
tions is proportional to the efficiency of the trans¬ 
ducer and is shown in Figure 66. The heavy curve C 
is the impedance locus in the absence of reflections; 
the curves A and B show the effect of reflection from 
an almost perfectly reflecting surface, with the dis¬ 
tance of the tran.sducer face from the surface very 
slightly different for the two loci. The curve D shows 
the effect of reflections from a surface that ab.sorbs 
most of the incident energy. The dimensions of the 
face of the transducer used for these loci were 
1.67 X 0.48 wave lengths at 26 kc. A transducer 
who.se face is small compared with a wave length 
shows only a change in the diameter of the imped- 
dance circle as the result of reflections, instead of 


.small circles, cusps, or indentations. A transducer 
whose face is two or more wave lengths in either 
dimension may exhibit more than one re-entrant cir¬ 
cle or cusp on the impedance circle, as in Figure 68, 
where one dimension of the face was about 6 wave 
lengths. 

Reflections can, of course, be avoided by working 
in open water where there are no reflecting surfaces, 
but it is more convenient to work in a tank where 
water conditions can be controlled. In a tank with 
steel walls the reflections are .such that impedance 
measurements are jn’actically im|)os.sible, but these 
reflections can be reduced l)y lining the tank with an 
absorbing material. Such a tank was built by the 
Bell Telephone Laboratories^' and proved useful 
in making impedance measurements with water 
loading. 

Since the walls of the ab.sorbent-lined tank do not 
absorb all incident sound, measurements in the tank 
are subject to some troubles with reflections. At 
normal incidence the .sound reflected from the surface 
of the tank walls is 17 or 18 db below the incident 
sound at 30 kc.'" The effect of this on one transducer 
has been illustrated in curve D of Figure 66, where 
the tran.sducer was facing the bottom of an ab.sorb¬ 
ent-lined tank. Figure 67 shows the changes in the 



F'igure 67. Graph of G and B vs distance from re¬ 
flecting surface. 


admittance of another tran.sducer at its frequency of 
maximum efficiency as the distance of the transducer 
face from the bottom of the tank was varied. From 
the magnitude of the.se changes and other data 
obtainable from the air and water admittance loci 
of the transducer, the reflection coefficient of the 
reflecting surface can be computed.'* The reflection 
coefficient computed for the tank bottom at 62 kc 


CONFIDENTIAL 































280 


.MEASlRE.Mt:NT OF ELECTRICAL CHARACTERISTICS 


is about 0.1, in agreement with the data given 
above. 

Effects of reflections in the tank can usually l)e 
eliminated by orienting the tran.sducer in the tank 
so that most of the radiation must be reflected more 
than once before it can return to the transducer, with 
a resulting increa.se in attenuation with each reflec¬ 
tion. The directional discrimination of the tran.sducer 
can be utilized to attenuate reflections further. How¬ 
ever, it is sometimes impossible to orient the trans¬ 
ducer at a skew angle with respect to all the reflecting 
surfaces. For example, when only the face of the 
transducer can be immersed, the reflections from the 
bottom of the tank return normal to the transducer 
face after only one reflection, resulting in a distortion 
of the impedance locus of a transducer ha\'ing fairly 


WITHOUT BAFFLE 



R IN 


■_ 4 _- 

I 


Figure 68. Effect of reflectii 
circle. 


WITH BAFFLE 



0 12 3 

IH MS 



) 


1^1 

s in tank on admittance 


high efficiency. Figure 68 shows the effect of such 
reflections. A remedy for this trouble is the use of a 
tank with a bottom that is not parallel to the surface 
of the water. The same effect can be obtained with a 
false bottom or reflecting baffle under the transducer, 
.so that the radiated sound is deflected against several 
absorbing surfaces before it can return to the trans¬ 
ducer. The improvement effected by a reflecting 
baffle, consisting of an air-filled metal box, is al.so 
shown in Figure 68. The efficiency of the baffle could 
be improved by incorporating in it some additional 
attenuation of the incident sound instead of simply 
using the nearlj’ perfect reflection from a water-air 
interface to divert the sound beam. 


9.2..5 Field Measurements 

When tran.sducers were too large to be iilaced in 
the absorl)ent-lined tanks for impedance measure¬ 
ments with water loading, these measurements had 
to be made at the HUSL field stations. For this pur¬ 
pose a portable admittance bridge was constructed. 
The circuit is essentially that of the admittance 
bridge of Figure 16, but the terminal box with its 
.switches, trimmers, and blocking condensers is omit¬ 
ted. The L & N resistor and capacitors are con¬ 
nected directly to the ratio box’s A and C terminals, 
and the unknown to the A or C terminal, according 
to whether it is inductive or capacitive. The change 
from inductive to capacitive measurement is made 
by .switching the connection of the unknown from 
one terminal to the other. 

The bridge components were mounted in a wooden 
frame and connected with bus wire. One of the de¬ 
tectors used with the admittance and impedance 
bridges was remo^'ed from the bridge console and 
u.sed with this portable bridge. The field stations 
provided suitable oscillators. 

The alignment of this bridge was similar to that of 
the admittance bridge, except that the only trimmers 
were those in the ratio box. When these trimmers did 
not have sufficient range, external resistors or ca¬ 
pacitors had to be added to the bridge, but this was 
.seldom necessary. When the decade capacitor was 
used, its residual capacity of about 70 n^l{ had to be 
offset by a slightly different alignment procedure than 
that used for the admittance bridge, since there is no 
separate trimmer for this compensation. The align¬ 
ment was made by means of the trimmers with the 
resistance box disconnected and the decade capacitor 
set at 0.001 /if acro.ss one arm of the bridge and the 
air capacitor .set at 1,000 /i/if across the opposite arm. 
The air capacitor was then connected in parallel with 
the decade capacitor for the measurements. If a 
10 ,000-ohm resistor was used acro.ss the unknown to 
bring the conductance within the range of the bridge, 
the alignment was made with this resistor and the 
resistance box set at 10,000 ohms connected to op¬ 
posite arms of the bridge. 

The accuracy of this bridge was ecpial to that of 
the admittance bridge used in the laboratory, but it 
was not so convenient to use because of the nece.ssity 
for changing the connections and realigning the 
bridge when a change was made from inductive to 
capacitive operation. The lack of blocking con¬ 
densers in the bridge was not a serious disadvantage 


CONFIDENTIAL 





















































PATTERN AND MEASUREAIENTS IN ABSORBENT-LINED TANKS 


281 


because polarizing current was seldom required in 
the field measurements. 

9.3 PATTERN AND FREQUENCY 
RESPONSE MEASUREMENTS IN 
ARSORRENT-LINED TANKS 

9.3.1 Methods 

The methods of calibrating transducers and meas¬ 
uring their frequency responses and patterns in ab¬ 
sorbent-lined tanks are the same methods as those 
used in open water at the field stations, and the 
equipment is similar.® Differences between tank 
mea.surements and open-water measurements residt 
from the small separation of source and receiver im¬ 
posed by the tank dimensions and from reflections 
from the tank walls. 

9.3.2 Equipment 

The tanks used for acoustic measurements in water 
were the absorbent-lined tanks constructed by the 
Bell Teleidione Laboratories.® One is shown in 
Figure 69. To the cover of the tank, as received from 
BTL, was added the apparatus for suspending and 
rotating the devices under test. At one end of the 
cover is a shaft which can be rotated by hand or at 
two speeds by motor. This shaft can be raised or 
lowered by a hand crank l)ut cannot be moved along 
the slit in the tank cover. At the other end of the tank 
is a similar shaft which can be raised or lowered, ro¬ 
tated by hand, and moved back and forth along the 
opening in the cover. The maximum jjossilde sepa¬ 
ration of the two shafts is about 18 in. Both .shafts 
are terminated in a standard 1-in. male pipe fitting. 
The shafts are hollow and a transducer may be 
supported by feeding its cable through the shaft. The 
left-hand transducer shown with the tank in Figure 
69 is an example. Special adapters have been made to 
attach transducers to the fittings on the shafts and to 
permit offsetting the transducer from the axis of the 
shaft. 

The equipment u.sed with the tanks in calibration, 
frequency-response, and pattern measurements is 
shown in Figure 70. The left-hand rack contains, 
from top to bottom, a New London measuring 
amplifier, a calibration amplifier, a heterodyne re- 

Only steady-state measurements have been made at 
Hl'SL. For the application of pulse methods to such meas¬ 
urements, see reference 19. 


ceiver, and the power supplies for the two amplifiers. 
The left center rack contains an o.scilloscope, with 
shelf space for additional instruments, such as the 
decade amplifier shown beside the oscilloscope in the 
photograph, a 10-kc frequency imdtiplier, and a 1-kc 
isolation amplifier, the lower part of the rack being 



Figure 69. BTL absorbent-lined tank. 

filled with blank panels. The right center rack con¬ 
tains a meter panel, an H-P oscillator Model 200-D, 
a Sound Apparatus Company’s automatic voltage 
level recorder, and the regulated power supplies for 
the oscillator and recorder. The right-hand rack con¬ 
tains an H-P o.scillator Model 200-CR, a noi.se gener¬ 
ator, a pu.sh-pull parallel 6L6 power amplifier, an 
output transformer panel, a cathode-follower power 
amplifier, and a space for storing standard hydro¬ 
phones and projectors. 

The New London measuring amplifier was con¬ 
structed for HUSL by the New London Underwater 


CONFIDENTIAL 

















2«2 


MKASUREME.NT OF ELECTRICAL CHARACTERISTICS 


Sound Laboratory. It is an excellent low-noise anipli- 
fier '• *■ with a inaxirninn gain of 80 db and provi¬ 
sion for inserting a calibrating voltage, but it was 
used only occasionally to supplement the calibration 
amplifier. 

The calibration amplifier was designed and built at 
IIUSL for use in calilwation measurements. It has a 
high-impedance input into a grid circuit and a low- 
impedance (100-ohm) input into a transformer. The 
transformer input can be either balanced or unbal¬ 
anced with respect to ground. A calibration voltage 
can be inserted in series with any of the injjutcircuits. 



Figure 70. Riick.s containing calibration equipment. 

The maximum voltage gain with the high-impedance 
input is 116 db,with the low-impedance input 109 db. 
The frequency respon.se is shown in Figure 71 and the 
circuit of the amplifier in Figure 72. An external 
electronically regulated power .supply is used with 
this amplifier. 

The heterodyne receiver is one of those con¬ 
structed at HUSL. It was used occasionally for lis¬ 
tening to the output of hydrophones. 

The shelf at the top of the left center rack can be 


used to .support two Du Mont Tyjie 224 oscillo.scopes 
or other apparatus. 

The 10-kc frecpiency multiplier supplies the tenth 
harmonic of the l,0C0-cycle standard signal for use in 
checking frequency. The circuit is similar to that of 
the multi])lier used with the bridges shown in Figure 
28. 

The 1-kc isolation amplifier was designed to elimi¬ 
nate the interaction between other circuits through¬ 
out the laboratory connected to the 1,000-cycle line 
and the mea.suring ecpiipment. An amplifier with a 
tuned circuit and several cathode-follower outputs 
was used to Isolate the equipment u.sing the 1,000- 
cycle signal from the line. The .subsequent introduc¬ 
tion of a low-impedance 1,000-cycle line throughout 
the building with Isolating re.sistors at each outlet 
made this isolation amplifier unnecessary. 

The meter panel provided a coin’enient means of 
.switching a Ballantine VTVM to any of the circuits 
u.sed in calibration or to external circuits. It also pro¬ 
vided a .switch for connecting the oscillator output 
to either the power amplifier or the calibration input 
of the calibration amplifier and for simultaneously 
connecting the voltmeter to the proper circuit. An¬ 
other .switch permitted the .selection of either fre- 
cpiency or rotation indexing controls for the marker 
circuit in the recorder. On the meter panel are 
mounted two 10 K resistors, the use of which will be 
discussed in connection with the use of the power 
amplifier to supply constant current to a projector. 
The circuit of the meter panel is shown in Figure 73. 

The H-P Model 200-D audio oscillator was modi¬ 
fied for use in calibration work. A dial drive was pro¬ 
vided to permit the rotation of the oscillator dial by 
the recorder drive in plotting a frequency response 
automatically. The dial could be rotated at either of 
two speeds by changing the connection of the flexible 
shaft to the recorder gear box. The two speeds cor¬ 
respond to the frequency range of 7 to 70 kc spread 
over either 15 or 24 in. of recorder paper. A frequency 
indexing signal is supplied to the marker circuit of 
the recorder by a relay in the recorder which is oper¬ 
ated by a photocell. A disk of the same size as the 
oscillator dial, mounted on the dial shaft behind the 
panel, and with small holes drilled around its circum¬ 
ference to correspond to the dial calibration marks, 
acts as a shutter between the photocell and a light 
source, so that the photocell operates the relay as 
these holes permit the light to strike the photocell. 
The photocell circuit is .shown in Figure 74. Its .sensi¬ 
tivity can be adjusted by a .shaft through the bottom 


C(4NFIDENTIAL 










PATTERN AND IMEASIREMENTS IN ABSORRENT-LINEI) TANKS 


283 




of the oscillator to the left of the dial. The leads to the 
relay-operated switch appear at the rear of the oscil¬ 
lator as a two-pronged Jones plug. The plate voltage 
of the photocell circuit can be turned off and on with 
the switch at the lower left corner of the oscillator 
Ijanel. A limit switch operated by the photocell disk 
shuts off the recorder motor when the high-frequency 
end of the dial is reached. The connection of the 
switch to the recorder is made by a cable emerging 
from the right side of the oscillator. 


The voltage control of the oscillator was altered to 
permit a finer control of the output voltage. The 
single potentiometer used in the original oscillator 
was replaced )iy the circuit of Figure 75. The two- 
position switch and the potentiometer with a loga¬ 
rithmic taper (Centralab N-115) ijermit the voltage 
to be set at any level without difficulty. These two 
controls are located at the upper right of the panel. 
The output voltage can also be varied by the inser¬ 
tion of a 35-db attenuator across the output termi- 


CONFIDENTIAL 





































































































































284 


MEASUREMENT OF ELECTRICAL CHARACTERISTICS 


TO ROTATION 
MARKER 


GR 

IT 


TO OSC MARKER 


marker 6,6 6 6 
SELECTOR ‘ 

SWITCH 


CABLE TO RECORDER 


CABLE TO 
OUTPUT OF 
POWER i 
AMP 


1^(0 


0 

BALLAimC 

VTVM 

f f 


SYMBOL 

o 

o 

INDICATES CANNON 
CONNECTOR 
MALE 




U 




GR 


eiOK 


>OK 


5oTi 6^> 6 io 6 5^ 


PROJECTOR VOLTAGE 
SWITCH 


L BALLANTINE 
/ SELECTOR SWITCH 

9 9 9 o 


Gi?. 

terminals 


IT- 

p « 




use-calibrate 

SWITCH 




TO CAl.lBRAT10^4 

AMPLIFIER 


TO OSCILLATORTD POWER 
AMP INPUT 


6J5 



Figure 74. Photocell marker circuit. 



Figure 75. Voltage control circuit in oscillator. 


Figure 73. Circuit of meter panel. 

nals, controlled by the switch beside the output 
terminals on the panel. This attenuator is shown in 
Figure 76. The oscillator’s original power supply has 
been disconnected, and an external electronically 
regulated power supplj' is used for greater stability. 

The circuit of Sound Apparatus Company’s voltage 
level recorder was changed considerably to improve 
its operation and extend its frecpiency range. The 
changes made in this instrument are discussed in 
Chapter 10, and circuit diagrams of the original and 
modified forms are given in Figures 32 and 33 re¬ 
spectively of that chapter. 

The H-P Model 200-CR o.scillator is used occasion¬ 
ally when frecpiencies above the 70-kc maximum of 
the other oscillator are desired. 

The noise generator is a source of broad-band 
thermal noise but was used very rarely in measure¬ 
ment work in the tanks. 

The push-pull parallel 6L6 power amplifier was 
used largely to drive a Brush Model C 13-2, 4 X 4-in. 
crystal transducer as a projector. Its high-impedance 
balanced output can, however, be used for other 
purposes, or by the use of an output transformer, such 
as the Western Electric W-28562, it can be used to 
drive lower impedances. The circuit of the amplifier 



OUTPUT 


1350 k 50 < 

-1-'-@ 

Figure 76. Attenuator pad in oscillator. 

is shown in Figure 77. In order to drive the Brush 
C 13-2 at a constant current as the freciuency varies 
with a constant voltage input to the amplifier, a 
compensating circuit had to be used in the input of 
the amplifier. The male Cannon connector permits 
the input to pa.ss through the compensating circuit, 
while the female connector feeds the following stage 
of the amplifier and permits the use of the amplifier 
with a relatively flat frequenc}" response. To obtain 
a constant current through the Brush C’ 13-2, two 
10 K resistors are connected in series with it, as in 
Figure 78, so that 'i^ariations in its impedance with 
temperature have little effect on the load on the 
amplifier. These resistors are mounted on the meter 
panel and can be removed from the circuit by the 
top switch. These 10 K resistors also permit the cur¬ 
rent through the transducer to be measured with the 
Ballantine VTVM. This is done by measuring the 
voltage drop across either of the two resistors. The 
top right-hand switch on the meter panel connects 


CONFIDENTIAL 










































































































Current in miluamps 


PATTERN AND MEASUREMENTS IN ABSORBENT-LINED TANKS 


285 



lOK 




Figure 79. Current through Bru.'^h C 13-2 v.s fre¬ 
quency. 


tlie Ballantine successively to the high end of one 
10 K resistor, to the low end of that resistor, to the 
high end of the other resistor, to the low end of that 
resistor, to one side of the transducer without the 
resistors in series, and to the other side of the trans¬ 
ducer as the switch is rotated clockwise. The current 
through the transducer as a function of freciuency is 
shown in Figure 79. 

The output transformer panel mounts a UTC 
LS-55 audio transformer designed to match push- 
pull parallel 6L6’s to various load imiiedances. The 
transformer impedance can be varied by a plug-and- 
jack system. The efficiency of this transformer is 
poor above 20 kc; the Western Electric W-28562 is 
much better at high frec[uencies. 

The cathode-follower power amplifier uses parallel 
GYG’s to provide a high-voltage, unbalanced output 
into a fairly low impedance. (The circuit is shown 
in Figure 80.) The amplifier was designed to drive 
the Brush C 13-2, but the balanced output of the 
other power amplifier was found to be more satis¬ 
factory for calibration work. 


CONFIDENTIAL 





























































































































































286 


MEASUREMENT OF ELECTRICAL CHARACTERISTICS 




Figure 81. Sound field vs frequency in absorlient-lined tank. A and B. Measured in tank under siqiposedly identical 
conditions. C. Measurements made at barge at 92 in. D. Measurements made in tank at 18 in. 


Some care wa.s taken in the grounding of this equip¬ 
ment to avoid troubles with ground loops in mea.sure- 
ments at low levels. The frame of the tank in Figure 
69 is grounded to the main laboratory ground bus 
bar. The two outside racks, containing the calibra¬ 
tion and power amplifiers, are grounded to the tank 
by two metal strips (Figure 70), which also serve to 
support cables running from the tank to the racks. 


The two center racks are grounded only through the 
cables connecting their apparatus to that of the other 
racks. 

9 . 3.3 Results 

Calibrations made in the absorbent-lined tank 
closely approximate those made in open water. The 


CONFIDENTIAL 




























































































PATTERN AND MEASUREMENTS IN ABSORBENT-LINED TANKS 


287 



Figure 82. Directivity pattern of Bru.sh C 13-2 at 
20 kc. 

agreement depends on frequency, separation, and the 
hydrophone and projector used in the measurement; 
the more directional the tran.sducers used, the smaller 
the effect of reflections in the tank. Figure 81 shows 
some typical sound fields as a function of frequency 
measured in the tank (curves A, B, and D) and one 
(curve C) measured in open water at the liarge with 
the same equipment used in the tank measurements. 
Measurements in the tank were not made under 
optimum conditions for the reduction of fluctuations 
in the field because of reflections, smce a bi-direc¬ 
tional pressure gradient hydrophone was used as a 
reference standard and the receiving hydrophone was 
located at the focus of reflections from the curved 
end of the tank. The open-water measurement was 
also made at a greater distance than that possible in 
the tank. However, even under these conditions, the 
maximum fluctuations amount to only 2 or 3 db. The 
reduction in fluctuations with an increase in fre¬ 
quency may be attributed both to an increase in the 



Figure 83. Directivity pattern of Brush C 13-2 at 

60 kc. 

attenuation of the tank walls and an increase in the 
directionality of the Brush C 13-2 transducer used 
as the itrojector (Figures 82 and 83). These curves 
also show the extent to which a flat field was achieved 
by driving the Bru.sh C 13-2 at a constant current. 

The effect of both reflections and the small sepa¬ 
ration of source and receiver are more evident in the 
measurement of directional patterns than in that of 
frequency response. The distortion of the patterns 
taken in the tank is considerable, particularly in the 
minor lobes and the rear radiation, as shown in 
Figures 82 and 83, and such measurements have only 
relative significance. However, in the development of 
transducers, the cpialitative information obtainable 
from tank measurements of directivity is useful in 
determining faults in construction, such as air bub¬ 
bles in the castor-oil filling, before time is wasted in 
more accurate measurements at field stations. 

The use of the tank for pattern and frequency re- 
spon.se measurements was confined largely to obtain¬ 
ing qualitative data rapidly, since field stations were 
available for more accurate and more reliable mea.s- 
urements in open water and at distances sufficiently 
large to approximate those u.sed in practice. 


CONFIDENTIAL 


















Chapter 10 

OPEN-WATER MEASUREMENT AT HUSL 


10.1 INTRODUCTION 

A complete investigation of the acoustic and elec¬ 
tric properties of transducers can be made only if 
facilities are available for testing the products of 
transducer research under conditions duplicating as 
nearly as possible those encountered in actual opera¬ 
tion. The realization of such conditions requires sujj- 
porting a transducer at any desired depth in water 
and at any orientation with respect to a free sound 
field. The production of a free field at the region of 
measurement is accomplished in practice liy a trans¬ 
mitter in open water at sufficient distance from that 
region so that nonuniformity in the wave caused by 
shape and directional selectivity of the transmitter 
is ineffective and at sufficient depth to prevent dis¬ 
turbances from reflections from the surface of the 
water. The facilities and procedures at HUSL for 
the determination of the acoustic characteristics of 
transducers are described in this section. 

Measurements of transducer performance in open 
water were first made at various Boston Harbor 
piers or on the USS Galaxy. Neither arrangement 
proved satisfactory. Because of various inconven¬ 
iences, the decision was made to build a field station 
with permanent installations for testing. A barge 
rather than a pier was chosen partly as a result of 
the experience of the New London Laboratory with 
its barge and partly in the expectation of having a 
measuring station that could be towed out into 
Boston Harbor away from noise and other disturb- 


ances. 


10.2 

CHARLES RIVER BARGE 

10.2.1 

Locations 


The Charles River barge was built by the Hodge 
Boiler Works of Boston, Massachusetts, and launched 
at the Hodge pier on March 31, 1942. The barge was 
first tied there and measurements were made in the 
water at this location for five months, but the site 
was very unsuitable because of noisy surroundings 
and rough waters. On September 3, 1942, the barge 


was moved to the lower Charles River Basin and 
located 150 ft off shore and about 500 ft upstream 
from the Charles River Dam. 

The exterior of the barge and of an auxiliary craft 
known as “Tippecanoe” is shown in Figure 1. The 
barge it.self was 61X21 ft, fabricated from Ct-in. 
tank steel, with about 18-in. draft and a displacement 
of 47 tons. It carried a cabin approximately 40 X18 
ft, with laboratory space 28X18 ft and living 
quarters for the crew of three. The hold provided a 
limited amount of storage space for equipment not 
in constant use. Shore power (110 volts a-c) and 
telephone connections were supplied by means of a 
submarine cable. A well 10X3 ft provided acce.ss to 
the water. At the bottom of the well were a pair of 
hinged steel doors which could be closed when the 
barge was being towed. 



Figure 1 shows davits for hoisting heavy ecjuii)- 
ment on board and the 6-in. I beam which extended 
inside the cabin over the fidl length of the well. A 
half-ton electric hoist, traveling along the I beam, 
made the handling of the heaviest transducers a 
fairly simple matter. An interior ^’iew of the labora¬ 
tory is given in Figure 2. 

10.3 “TIPPECANOE' 

This craft is shown alongside the Charles River 
barge in Figure 1. It was originally built for develop- 


288 


CONFIDENTIAL 






SPY POND STATION 


289 


inent work and was nothing more than a barrel float 
with a shed on it. A wood deck 31 X 15 ft was 
strapped to three cylindrical tanks 12 ft long by 3 ft 
in diameter. The deck house was 18 X 10 X 8 ft. 
Its equilibrium was unstable, hence its name. Two 
openings through which transducers could be lowered 
into the water were cut in the floor 6 ft apart. 



Figure 2. Interior of the iiarge laboratory. 


It also .served a useful purpose for the demonstra¬ 
tion of projector tent gear [PTCi].-' For this use, a hoist 
gear similar to the standard QC’ hoist, by means of 
which the projector to be tested was lowered into the 
water, was built over one of the wells. Pattern and 
response measurements were made with the sound 
gear monitor\_SGM~]d^ During 1944 “Tippy” .served a 
Uiseful purpo.se in training Xavy personnel in the tech¬ 
nique of projector testing. 

10.4 SPY POM) STATION 

After about a year of operation at the barge, the 
expanding program at IIUSL called for increa.sed 
measuring facilities. The size of the barge well and the 
awkward means of getting very large units on lioard 
imposed a serious limitation on the size of devices 
that could be tested. No object greater than 19.5 in. 
in diameter could be put in the sound field without 
considerable difficulty, and measurements at dis¬ 
tances greater than 8 ft could be made onlj^ by tem¬ 
porary rigging of the sound .source from the barge 
deck outside the cabin. In order to meet the recpiire- 
ments of the ordnance division of the laboratory, a 
measuring station to which equipment coidd be de¬ 
livered directly from trucks was desirable. A number 
of lakes and ponds within a radius of 16 miles of 


HUSL were investigated and fortunately the one best 
suited for the purpose was found at Spy Pond in 
Arlington (.'enter, only 'S}/o miles away. 



-V rough sketch of the pond is given in Figure 3. 
Soundings of the pond showed that the eastern shore 
and the shore of the island drop off sharply to a depth 
of 40 ft. The remaining shore has a more gradual 
slope. A contour of the bottom and an elevation of 
the station as finally built are shown in Figure 4. No 
.serious acou.stic difficulties due to reflection of sound 
from the adjacent shore were encountered during the 
two years of the station’s operation. 

Plans for the station were based on exjierience with 
the limitations of the barge facilities as well ason ideas 
solicited from the various HF^SL groups interested in 
acoustic mea.surements. The specifications for the 
building called for a frame structure 20 X 32 ft, with 
two 16-in. 50-lb steel I beams, spaced 4 ft apart, run¬ 
ning on either side of the centerline the full length of 
the building. The lower flanges of these beams served 
as a track for the dolly on which tran.sducers were 
carried along the well and from which they could be 
mounted on the vertical shaft for lowering into the 
water. A structural feature consisted of two 12-in. 

1 beams running acro.ss the ceiling, spaced 12 ft apart, 
each carrying a one-ton electric hoist. A platform 

2 ft wide extended across the water front of the build¬ 
ing. .\n apron of planking nailed to the bottom, 
framing timbers around the whole outside of the 
building and extending 6 in. below the surface of the 
water, served as a windbreak for the space between 
the water and the floor. 

The general layout of the station Ls .shown in 


CONFIDENTIAL 








290 


OPEN-WATER MEASUREMENT AT HUSL 





Figure 6. General view of Spy Pond laboratory. 


Figure 7. Front view of Spy Pond laboratory. 


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HANDLING EQUIPMENT 


291 


Figure 5. Heavy equipiuent up to 24 ft in length 
could be handled with comparative ease by means of 
dollies running on the ramp from the shore to tlie 
station. Photographs of the exterior are shown in 
Figures 6 and 7. 


10.5 HANDLING EQUIPMENT 

C'.ood measurement technique involves setting up 
a sound field in the water and placing the transducer 
to be measured at a known fixed point in this field. 
For this purpose precise means are needed to deter¬ 
mine the depth and orientation of tlie sound source 
and of the receiver and their exact location in the 
water relative to each other. In the early days at the 
barge, this was done in somewhat primitive fashion 
by mounting jn-ojector and receiver at ends of 1-in. 
pipe. The depth of the projector was determined by 
direct measurement from a fiducial mark on the 
supporting pipe to the transducer. The depth of the 
receiver was adjusted accordingly by means of a 
collar clamped to its pipe support, with the collar set 
in a pipe clamp fastened on the edge of the well. In 
the summer of 1943 an improved gear for the barge 
was developed which, with the necessary modifica¬ 
tion, was essentially the same as that installed at 
Spy Pond. The 1-in. pipes, which quite often proved 
not to be straight, were replaced by 14 ft .sections of 
.selected nickel-plated tubing 2'j^ in. in diameter, 
each terminated by a 6-in. flange with four slots 
and hinged bolts for attaching a shorter flanged .sec¬ 
tion that carried the tran,sducer. The arrangement is 
clearly .shown in Figure 8, which is the receiver mount 
at Spy Pond. 

A number of special adapters and clamjjs to take 
care of the different ty]ies of tran.sducer mountings 
were designed. Some of these are shown in Figure 9. 
The shaft was raised and lowered by means of a half¬ 
ton electric hoist in the peak of the roof. (The steeple 
on the barge in Figure 1 was added to permit this 
arrangement.) The hoist was controlled by light 
cables running down from the motor .switcli. The 
shaft was graduated in half-inch intervals about 9 ft 
of its length. The zero point was 5 ft above the bot¬ 
tom surface of the flange when the latter was at the 
surface of the water. The distance from the bottom 
of the shaft flange to the midpoint of the tran.sducer 
was mea.sured directly, so that the submersion depth 
was the reading on the scale on the shaft plus this 
measured distance. A .scale giving the distances be- 


twetm the transmitter and receiver shafts was marked 
on the track that carried the transmitter .shaft. 

The transducer was oriented with reference to a 
fiducial mark on the shaft running along its length 
and a fixed mark on the sleeve through which the 
.shaft passed. Alignment of the face of the tran.sducer 
with the fiducial mark could be made by eye with a 
precision of ± 2 degrees. A more precise orientation 
of a transducer with reference to a circular .scale on 



Figure 8. Transducer mount at Spy Pond. 


the disk that is shown in the illustration, which could 
be clamijed to the shaft, could be made by acoustic 
means provided the transducer gave a sharjj beam 
riidiation pattern. The shaft was rotated by clamp¬ 
ing it to the disk-and-pulley a.s.sembly, which was 
belt-connected to a 'lo-hp motor. The rotational 
speed was one revolution in 98 sec. 

A similar but somewhat simpler arrangement for 
the jirojector mounting is shown in Figures 10 and 
11. Here the raising and lowering were effected by 
means of a hand winch and steel cable. The cable was 
attached to the bottom rather than to the top of the 
shaft. In Figure 10 a steady bearing may be seen 
down close to the water, while at Spy Pond vertical 
alignment of the shaft was insured by bearings at the 
top and bottom of the pyramidal frame that carried 


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292 


OPEN-WATER MEASUREMENT AT IIUSL 





OLD B-I9B TYPE 


RAT TRAP 
B-I9B HOLDER 


Figure 9. Tnuisducer clamps and adaiiters. 


the sliaft. The means for controlling the depth and 
orientation were the same as in the mounting for the 
receiver. 

In Figure 12 is shown the device used at Spy Pond 
for making pattern measurements on a hydrophone 
that is offset from the axis of the body in which the 
hydrophone is mounted. A sturdy 3.5 X 4-ft frame 
made from steel angles supports a coordinate pair of 
carriages, movable in directions at right angles to 
each other. The inner carriage carries a flange 
supporting the body in which the hydrophone is 
mounted. By adjustment of the positions of the car¬ 
riages, the face of the hydrophone can be brought 
into the axis of rotation, thus giving a true radiation 
pattern of the mounted hydrophone. 


10.6 MEASUREMENT OF TRANSDUCER 
CHARACTERISTICS 

For full knowledge of the performance of a tran.s- 
ducer used as a receiver, the following data are 
needed: (1) open-circuit sensitivity, (2 ) receiving re- 
spon.se, (3) impedance, and (4) radiation iiattern. 

For a transducer used as a projector, the transmit¬ 
ting response, that is, the sound pressure set up at a 
standard distance (usually 1 meter) for a stated 
electric input, is also required. The meanings of the 
above terms are discussed in Chapter 1, where it has 
been .shown that the efficiency (ratio of acoustic 
power output to electric power input) can be com¬ 
puted from the measured values of these cpiantities. 


CONFIDENTIAL 






MEASUREMENT OF TRANSDUCER CHARACTERISTICS 


293 



Figure 11. Projector shaft ami carriage at Spy Pond. 


Figure 10. Projector .shaft and carriage at the barge. 

Sensitivity is ordinarily expressed in decibels re¬ 
ferred to a unit sensitivity of 1 volt per dyne per sq 
cm and .sound ])re.ssnre level in decibels referred to 
1 dyne per ,sq cm. 

10 . 6.1 Measurement of Sound 

Field with Standard Hydrophone 

The fundamental measurement for the determina¬ 
tion of all the foregoing is the measurement of in¬ 


tensity of the sound at a given ixiint in the .sound 
field. Since all the characteristics of a transducer are 
functions of the frequency of the sound, knowledge 
of the frequency is also es.sential. An approach to the 
general procedure followed in acoustic mea.surements 
at HUSL can liest be made by a detailed account of 
the measurement of the sound-pre.ssure level by 
means of a calibrated hydrophone, that is, one of 
known sensitivity. The arrangement is shown sche¬ 
matically in Figure 13. 

The electric signal is supplied by a continuous fre¬ 
quency oscillator through a variable-gain amplifier 
and output transformer to the standard transmitter, 
which generates a pnre-tone acoustic signal whose 
frequency can be varied by movement of the fre¬ 
quency dial of the oscillator. The sound is picked up 
l)y the calibrated hydrophone, and the generated 
voltage is amplified by the variable-gain receiving 
amplifier, the output of which feeds into the voltage- 
level recorder. Certain preliminary adjustments are 
first made. The transmitting and receiving hydro¬ 
phones are varied in depth and azimuth until a 


CONFIDENTIAL 









29i 


OPEN-WATER MEASUREMENT AT HUSL 



Figure 12. Off-center transducer mount. 


niaxiimim output i.s shown on the vacuum-tube volt¬ 
meter I'l at. some convenient frequency in the range 
to be covered. Next, the gain controls of the trans¬ 
mitting and receiving amplifiers are set so that the 
recorded voltage level will fall within the 40-db range 
on the recorder tape over the entire frequency range. 
Gain-control settings on both transmitting and re¬ 
ceiving amplifiers are not changed during the further 
course of the measurements. 

The recorder driving mechanism is then mechan¬ 
ically connected to the frequency control dial of the 
oscillator, initially set at the lower end of the fre¬ 
quency range to be covered. The recorder is turned 
on, driving the o.scillator dial through the desired 
range of frequency and giving a trace on the recorder 
tape (respome curve shown in Figure 14A). The curve 
recorded on the tape is a function not only of the 
pre.ssure level of the .sound field but of the gauis of 
the receiving amplifier and the recorder. The shape 
of the response curve depends upon the frequency 



Figure 13. Schematic of arrangement for measure¬ 
ment of field. 


characteristics of both, as well as upon variation of 
the field with frequency. 

A voltage calibration of the amplifier and recorder 
is needed to find the actual voltage level of the stand¬ 
ard hydrophone output. In Figure loA the trans¬ 
ducer is represented as a voltage generator Et with 
internal impedance Zt terminated by the high-input 
impedance Zl oi the receiving amplifier. In making 
the voltage calibration, the .sound is turned off and a 
calibrating resistor 74 is inserted in the transducer 
circuit, as shown in Figure 15B. 

The resistance IE is much smaller than Zt. The 
calilirating voltage is measured by first reading the 
voltage output of the o.scillator on a vacuum-tube 
voltmeter and then connecting the oscillator through 
the attenuating network, whose attenuation has been 
previously measured, acro.ss the resistor IE- The at¬ 
tenuator pad is designed to give a range of attenu¬ 
ations in 10-db steps, so that the applied calibrating 
voltage level in decibels is known from the measured 
voltage of the o.scillator and the attenuator .setting. 
The calibrating voltage is chosen to give a recorder 
trace either above or below the response curve when 
the o.scillator dial is moved over the frequency range 
of the response curve. The calibration curve on Fig¬ 
ure 14A was obtained in this way and is the locus of 
points on the recorder tape corresponding to an ap¬ 
plied voltage level of — 75 db vs 1 volt at the indi¬ 
cated frequencies. 

The voltage level generated by the sound in the 
standard hydrophone is obtained from the two 
curves. The horizontal spaces on the tape correspond 


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MEASUREMENT OF TRANSDUCER CHARACTERISTICS 


293 



Figure 14. A. lle.spon.se and voltage caliliration of 
standard in measurement field. B. Receiving response 
and voltage calibration of test transducer. C. Receiv¬ 
ing pattern of test transducer. 

to a 1-db difference in the voltage level. Thu.s the 
voltage level of the respon.se at 40 kc is — 75 — o = 
— 80db referred to 1 volt. By carrying out the subtrac¬ 
tion for the series of frequencies, data are obtained 
for the voltage response curve of the standard trans¬ 
ducer in the sound field. It should be re-einphasized 
that no change is made in the gain in the receiving 


circuit between the taking of the response and the 
voltage calibration curves. 

When the voltage response of the calibrated hy¬ 
drophone is known, the sound-pressure level is easily 
obtained from this and the known .sensitivity of the 
hydrophone. 




AMPLIFIER 



RECXDROER 



ISI 


4 ' 






A 



B 

Figure 1.5. Schematic of voltage calibration. 


The sensitivity = volts per dyne per sq cm 

Sensitivity (db) = voltage level (db) — pressure 
level (db) 

Pressure level = voltage level — sensitivit}" (db) 

The .sensitivity of the standard used in this par- 
t icular case at 40 kc was — 112.9 db. Hence the sound- 
pre.s.sure level was —80 — (—112.9) = 32.9 db vs 
1 dyne per .sq cm. Since the pressure level equals 
20 log p, the pressure at 40 kc is log~^ 1.645, or 43 
dynes ])er sq cm. 

The frt'ciuency at each point of both the response 
and calibration curves is given by the vertical breaks 
in the curves. These are made by electric signals 
originating at the frequency dial of the oscillator as 
it moves over the frequency range. Details of .some 
of the frequency marker circuits used will be given 
later. 

10.6.2 Transmitting Response Curve 

Definitions of the various transmitting responses 
of interest were given in Chapter 1. The procedure 
followed in measuring the field is essentially the same 
as would be used in measuring the transmitting re- 
.sponse of a projector. For example, the current trans¬ 
mitting response of the projector, used in obtaining 
the curves of Figure 14A, could be found if the value 


CONFIDENTIAL 




















































296 


OPEN-WATER MEASUREMENT AT IIUSL 


of the current supplied to the projector to produce 
the field and the distance from projector to h^alro- 
phone were known. By definition, 


Current transmitting response = 


Px 

1 ’ 


where p\ is the rms sound pressure produced at 1 
meter when a current of / amp flows through the 
transducer windings. The pressure is a.ssumed to vary 
inversely as the distance from the source. If p is the 
pressure measured at a distance r, then 


/-'I • • P^ 

Current tran.smittmg response = — • 


Similarly, the voltage transmitting response can be 
measured by making simultaneous measurements of 
the input voltage across the projector and the field 




Figure 16 . Equivalent circuits of transducer and cable. 


at a known distance. If, for example, the voltage 
across the terminals of the projector had been main¬ 
tained at a constant known value as the frequency 
varied, a voltage transmission curve for the pro¬ 
jector could be deduced from the curves of Figure 
14A. 


10 .6..3 Measurement of Receiving 
Sensitivity 

Determination of the receiving sensitivity of a 
transducer involves a further set of measurements 
with the unknown transducer placed at the same 
point in the .sound field as was occupied by the stand¬ 
ard. Conditions at the tran.smitting end are to be kept 
unchanged, and response and calibration curves are 
to be taken exactly as in the ca.se of the standard. 
Such curves for a transducer having a resonance peak 
at 60 kc are shown in Figure 14B, The voltage level 
generated in the windings of the unknown is com¬ 
puted from the calibrating voltage and the difference 
of level on the tape between the response and calibra¬ 
tion curves. Again the sensitivity of the unknown 
transducer is obtained by di^dding the generated 
voltage by the sound pressure producing it or, ex- 
pre.ssing the sensitivity in decibels, by subtracting 
the pressure level in the field from the voltage level 
generated in the tran.sducer windings. To illustrate 
the calculation procedure, the sensitivity at 60 kc of 
the transducer for which the response is shown on 
Figure 14B is computed in detail. 


/?, (Resp. of 



Rx (Resp. of 


stand.) = 

16 

db 

hvd.) = 

31 db 

C, (Cal. of 



Cx (Cal. of 


stand.) = 

20 

db 

hyd.) 

33.0 db 

R, -C, 

- 4 

db 

Rx - Cx 

- 2.5 db 

C..,(Cal. volt.) = 

- 75 

db 

Cxx 

— 50 db 

Rs - C, + C,.. = 

- 79 

db 

Rx -Cx+ Cxx = 

— .52.5 db 

Sens, of stand. = 

- 112.4 db 

- Field 

- 33.4 db 

Field (db vs 1 



Sens, (db vs 1 


dyne per cmb = 

3.3.4 


volt per dyne 
per cnF) = 

- 85.9 


The effect on the receiving response curve of the 
impedance in which the receiver is terminated has 
been indicated in Chapter 1. In the measurements 
just described, the open-circuit sensitivity of the 
standard was used and since in all the measurements 
the receivers were terminated in the high input im¬ 
pedance of the receiving amplifier, it was the open- 
circuit sensitivity that was measured. A further 
point to be noted is that voltages are measured not 
at the transducer terminals but at the end of the 
measuring amplifier. 

In general, magnetostrictive transducers have rela¬ 
tively low impedances, so that the shunted capacity 
of the leads produces a negligible error in the meas¬ 
urements at frequencies below 70 kc. Crystal trans¬ 
ducers, on the other hand, have high impedances and 
the voltage mea.sured across the cable terminals may 
differ materially from that generated by the trans- 


CONFIDENTIAL 























MEASURING EQUIPMENT 


297 


duoer. In such cases, a measuring amplifier with a 
very high impedance {Zl > 17 Zt) may be used. If 
under these conditions the calibrating voltage is ap¬ 
plied directly across the input terminals of the 
amplifier, with the transducer shorted out, the error 
is less than 0.5 db. When it is necessary to measure 
the open-circuit voltage developed by a high imped¬ 
ance transducer with no cable attached, the procedure 
indicated in Figure 16 may be followed. The imped¬ 
ance of the cable is Xc. 

Figure 16A is the equivalent circuit of the trans¬ 
ducer and cable when sound is being received from 
the water. When a series-calibrating voltage is in¬ 
troduced, the situation is as shown in Figure 16B, and 

e' - E,. 

If Zz,» Zt or Zc, and Ec is adjusted to give the 
same output from the mea.suring amplifier as given 
by the sound signal, then e = e'. From Figure 16A, 

e = e' ^ Et - = Ec 

or 


To evaluate Et both the cable capacity and the trans¬ 
ducer impedance must be known by independent 
measurements. 

10.6.1 Pattern IVIeasurements 

Receiving patterns are usually taken while the re¬ 
ceiver and projector are still oriented as in taking 
the frequency response. The gain control of the re¬ 
ceiving amplifier is set to give a maximum le^'el of 
about 35 db on the tape with the oscillator set at the 
frequency at which the pattern is to be measured. 
The graduated disk is clamped to the rotor shaft 
with the zero of the scale at the fixed index. The shaft 
and transducer are then rotated slightly more than 
180 degrees from this position. The recorder-marking 
circuit is switched to the microswitch, operated by 
notches cut in the edge of the rotor disk so that mark¬ 
ings on the recorder tape now correspond to angles 
measured from the initial orientation of the tran.s- 
ducer. The recorder and the motor driving the ro¬ 
tator are turned on simultaneously and allowed to 
run through a complete revolution of the transducer. 
The receiving pattern is thus recorded as a function 


of the angle of orientation measured from the posi¬ 
tion of maximum response (Figure 14C). 

The transmitting pattern is similarly measured, 
starting from the arrangement of projector and re¬ 
ceiver for getting the transmitting frequency re¬ 
sponse. The transmitting pattern is obtained by 
rotating the transducer and recording the electric 
output of the receiving standard hydrophone, which 
remains stationary. 


10.7 MEASURING EQUIPMENT 

The bare e.ssentials of equipment needed for 
acoustic measurement and transducer calibration are 
indicated in Figure 13. The original equipment at the 
Charles River barge \vas little more than this. The 
elaboration of the transducer development program, 
the nece.ssity for time-saving devices, and the design¬ 
ing of special apparatus for specific types of measure¬ 
ments resulted in the addition of considerable acce.s- 
sory equipment. In general this was the same in the 
two stations, with minor variation dictated by the 
division of labor between the two. 

An idea of the overall final arrangement at the 
Charles River barge Is obtained by reference to Fig¬ 
ure 17. The essential features, with certain additions, 
were duplicated at Spy Pond (Figure 18). An impor¬ 
tant detail not shown in the photographs is thatallthe 
racks at the barge were on Lord resilient mounts. At 
both stations, difficulties with spurious grounds and 
resulting ground loops were encountered. These were 
particularly troublesome at the barge. The provision 
of a positive common ground, consisting of a mass of 
metal resting on the pond bottom and connected by 
a heavy cable to a brass plate mounted on the wall 
behind the racks, gave the versatility of grounding 
needed to eliminate ground loops at Spy Pond. The 
electric isolation of the racks from one another and 
from the steel hull was an additional requirement at 
the barge. A second feature of importance in the 
precision of measurement was the mstallation of a 
voltage regulator to control fluctuations of the main 
110-volt 60-cycle power supply. This, together with 
electronically regulated power supplies for the sepa¬ 
rate oscillators (Figure 19), gave the measuring sys¬ 
tems a high degree of stability. 

The individual elements of the final complete sy.s- 
tem at the barge are listed below Figure 17. Descrip¬ 
tion in detail will be given only of such elements as 
contain special features. 


CONFIDENTIAL 





298 


OPEN-WATER MEASUREMENT AT IIUSL 



HEWLETT-PACKARD 
OSCILLATOR 

BALLANTINE 2 


POWER SUPPLY FOR 
HEWLETT- PACKARD 


POWER SUPPLY FOR 
RECEIVING AMPLIFIER 


POWER SUPPLY 
FOR ANALYZER 


POWER SUPPLY FOR 
RECEIVING AMPLIFIER 


BATTERY BOX 


LEEDS AND NORTHROP 
SPEEDOMAX RECORDER 


TUNING UNIT 

WE I73D TRANSFORMER 

PATCH CORD BAY 

GENERAL RADIO 
OSCILLATOR. 


BALLANTINE I 


SOUND APPARATUS 
RECORDER 


WE I7B OSCILLATOR 
BATTERY CHARGER 


TRANSMISSION 
MEASURING SET 


15-WATT POWER AMPLIFIER 
90-WATT POWER AMPLIFIER 


DRIVING UNIT WITH 
POLARIZING CURRENT 


SUPPLY FOR CATHODE 
FOLLOWER HYDROPHONES 

SUPPLY FOR LAMP FOR 
FREQUENCY MARKER 


RECEIVING AMPLIFIER 
CALIBRATION ATTENUATOR 
FILTERS 


ANALYZER 


POWER SUPPLY FOR 90-WATT 
POWER AMPLIFIER 


Figure 17. Complete measuring equipment at the barge. (Note: Ballantine 2 is somewhat to left of arrow.) 


10.7.1 Sound Generating System 

The source of a-c current for frequencies up to 
72 kc originally used at the barge and throughout at 
Spy Pond was the Hewlett-Packard 200-D oscillator. 


The H-P 200-C (20-200,000 cycles) was a standby 
source for occasional measurements above 70 kc. The 
latter was not rack-mounted. In the early days, the 
markings of the frequency dial of the oscillator were 
taken at their face value. Where greater frequency 


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MEASURING EQUIPMENT 


299 



Figure 18. Complete measuring equipment at Spy Pond. 


precision was required, the (General Radio 713-B 
oscillator was used for frequencies up to 40 kc. Early 
in 1944, Western Electric 17B oiscillators became 
available and one of these was installed at the barge 
but not at Spy Pond. A very precise tuning-fork 
frequency standard (described later) was installed for 
frequency checking at both stations. 

Alodifications of the oscillators were made to 
adapt them to our use. The first was designed to pro¬ 
vide means for marking the frequency of the signal 
on the recorder tape. Various mechanical and electric 
devices, more or le.ss satisfactory, were tried, but the 
photoelectric device described here and used at Spy 
Pond proved the most reliable. 

It was necessary to move the frequency dial a few 
inches out in front of the chassis to allow room for the 
frequency indexing mechanism. A brass disk, slightly 
larger than the main tuning dial, was mounted on the 


tuning shaft between the panel and the cha.ssis. Small 
holes were bored near the edge of the disk coinciding 
with the frequency index marks on the main tuning 
dial. A pinhole lamp was mounted on one side of the 
disk so that when the disk rotated a flash of light was 
directed at a Type 922 photoelectric cell, which was 
mounted on the opjiosite side of the disk, every time 
a frequency index mark was passed. The impulse 
from the cell ojjerated a relay that jogged the record¬ 
ing pen, thus making a frecpiency indication on the 
recorder tape. 

To obtain a finer control of the power output of 
the H-P oscillator the gain-control potentiometer was 
replaced by a voltage divider. An attenuator pad 
designed to give an additional attenuation of 35 db 
was also built into the outjiut of the oscillator to 
serve when a very small amount of power was de¬ 
sired. 


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OPEN-WATER MEASUREMENT AT IIUSL 





Figure 19. Klcctronically regulated power supply. 



Figure 20. Frequency marking device on WE 17B 
oscillator. 


The mechanism for continuously varying the fre- 
ciuency of the oscillator consisted of a worm gear, 
driven by a flexible .shaft from the soiind apparatus 
recorder (described later), that engaged a gear 
mounted on the tuning condenser shaft of the oscil- 



Figure 21. Thyratron circuit for frequency marking 
on 17B o.scillator. 


lator directly behind the tuning dial. The worm gear 
was mounted on a pivoted support so that it could 
be engaged or not as desired. A limit microswitch 
actuated by a projection on the frequency indexing 
dial stopped the motor drive of the recorder at the 
upper frequency limit of the o.scillator. The mechan- 


CONFIDENTIAL 

































































































MEASURING EQUIPMENT 


301 


Motor Switch Diagram 


Il5v A C 



Figure 22. Circuit for synchronizing 17B oscillator and Speedomax recorder. 


ical connection lietween the oscillator and recorder 
is shown in Figure 17. 

The power supply of the oscillator was removed 
and replaced by the external voltage-regulated sup¬ 
ply shown in Figure 19. The supply of the oscillator 
as furnished was found to be too unstable to give the 
desired frequency stability. The oscillator and its 
power supply had to be isolated from the racks elec- 
tricallyby plastic grommets placed over themounting 
screws so that the oscillator would not introduce a 
second ground in calibration procedures. 

The installation of the frecpiency marker in the 
17B oscillator was .somewhat more complicated than 
in the Hewlett-Packard. The frequency scale in the 
former is approximately linear and is etched on a 
celluloid tape illuminated from behind. The photo¬ 
electric scheme u.sed is indicated in Figure 20. A 
G-volt bulb and a 922 photocell were mounted inside 
the oscillator on opposite sides of the frequency 
tape, all parts being blacked out .so that only a nar¬ 
row beam of light j^a.ssed through one edge of the 
tape onto a small patch of the active surface of the 
cell. Small spots or masks of Movietone film lacquer 
were painted on the frequency film in order to inter¬ 
cept the light at the points where frequency signals 
were to be giv'en. Details of the thyratron circuit 
that activated the marker pen are shown in Figure 
21 . 

Synchronism of the Western Electric oscillator with 
the Leeds & Northrup voltage level recorder used 
at the barge was effected by means of the arrange¬ 


ment shown in Figure 22. The shaft of a small syn¬ 
chronous motor, connected as shown to the driving 
motor of the recorder, were geared to the frequency 
control shaft of the oscillator. The speed with which 
the frequency varied was thus controlled by the 
recorder speed. In order to reduce the normal output 
of the oscillator (0.7 to 21 volts at 20 kc) two 20-db 
attenuating pads were built into the oscillator output 
circuit. 

10.7.2 Driving Amplifiers 

For most of the measurements the power supplied 
by the HUSL Type 33 15-watt amplifier was suffi¬ 
cient. A circuit diagram is shown in Figure 23. The 
input impedance is approximately 0.1 megohm and 
the output at 35 kc about 10,000 ohms. The barge 
equipment included in addition a 90-watt amplifier, 
shown in Figure 17. The circuit diagram of the am¬ 
plifier, with its power supply, is shown in Figure 
24. Ordinarily it was drh'en by the Type 33 unit. A 
third special amplifier was designed and built by the 
Spy Pond crew, primarily to give constant-current 
driving to the crystal projectors that were originally 
used in measurement. Owing to the decrease with 
frequency in the impedance, the transmitting re¬ 
sponse of a crystal tran.sducer has a rising frequency 
characteristic. The nominally constant-current am¬ 
plifier (Figure 25) .supplied a current to the Brush 
C-13 X-cut crystal tran.sducer that varies by only 
about 20 per cent from 8 to 70 kc. 


CONFIDEINTIAL 



























302 


OPEN-WATER MEASUREMENT AT HUSL 







Figure 24. Circuit diagram of the barge’s 90-watt 
amplifier. 


10.7.3 Output Transformer 

For the efficient transfer of electric power from the 
amplifier to the projector, the Western Electric 
173-D output transformer was used with the lower- 
powered amplifier. This is designed to match push- 
pull parallel 6L6 tubes to various loads. Its rated fre¬ 
quency range E from 35 to 15,000 cycles, but it Is 
downjbj' a matter of only a few decibels at 70 kc. 
The transformer with switching arrangements was 
rack mounted (Figure 17). Nominal impedances of 
7.5, 17, 30, 125, and 500 ohms could be selected. A 
1-ohm resistor inserted in the transducer circuit al¬ 
lowed driving current measurements to be made. 

Three output transformers for the 90-watt ampli¬ 
fier provided six possible output impedances of 2, 8, 
20, 80, 200, or 800 ohms. The secondary of each 
transformer had two sections. They showed imped¬ 
ances of 2, 20, or 200 ohms connected in parallel, and 
8, 80, or 800 ohms in series. 

10.7.4 Receiving Systems 

In the original installation at the barge and in the 
final installation at Spy Pond, a preamplifier giving 
a 40-db gain and a final amplifier with a 70-db gain 


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MEASURING EQUIPMENT 


303 


C«A«*n 



were jjrovided. Circuit diagrams of these are shown 
in Figures 26 and 27. Tiie input impedance of the 
preamplifier was 50 ohms. A high-pass filter was in¬ 
serted in the output to attenuate frequencies below 
150 cycles per second. The low side of the input of 
the final receiving amplifier was rewired to include 
General Radio terminals, as shown in Figure 28. 
There were two gain controls in this amplifier. That 
between the first and second stages was in two steps, 
each giving 30 db of attenuation. The one between 
the second and third stages was a Daven potenti¬ 
ometer covering 40 db in 2-db steps. 

The attenuator (Figure 29), for controlling the 
calibrating voltage indicated in Figure 15, was a 
separate unit with GR output terminals to plug into 
the input circuit of the amplifier, as shown in Figure 
28. 

The single 110-db amplifier designed and built for 
final installation at the barge is .shown in Figure 30. 



Both high and low impedance input circuits were 
balanced to ground, and the calibrating voltage was 
injected at the midpoint. The high impedance input 
was mounted in a separate cha.s.sis not carried on the 
relay rack. With certain transducers, there was at 


CONFIDENTIAL 




























































































































:m 


OPEN-WATER MEASUREMENT AT IIUSI 


6SJ7 350 .01 



Figure 27. Spy Pond measuring final amplifier. 



INPUT 



POSITION 

1 

2 

3 

4 

ATTEN UATION (db) 

4 6 

60 

80 

94 


Figure 28. Voltage calibration input circuit. Figure 29. Spy Pond voltage calibration attenuator. 


CONFIDENTIAL 



























































































































































































I39A 

IN^UT 


MEASURING EQUIPMENT 


305 



I2SH7 



>2SH7 liSM7 

_6 


I2SH7 


I60QA 

——►“ + 

290V OC 


Figure 30. Barge's 110-db receiving amplifier. 




Figure 31. High- and low-pass filtei*s used at the barge. 


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:m 


OPEN-\^ ATER MEASUREMENT AT HUSL 


A-C amplifier 


DETECTOR 


D-c amplifier and clutch 



6J5 


I IGURE 32. Original circuit diagram of sound apparatus recorder with enhancer. 


6SF5 


6SF5 


6S07 


6N7 



2-PRONG JONES PLUG 


Figure 33. Circuit diagram of revised sound apparatus recorder. 


CONFIDENTIAL 


CLUTCH 

COILS 
















































































































































































































































MEASURING EQUIPMENT 


307 


times serious interference from long-wave radio 
signals originating at a nearby station. This was 
eliminated by a set of filters designed to be inserted 
in the receiving circuit l^etween the receiving ampli¬ 
fier and the recorder. Included in it were two high- 
pass filters with cutoff at 1 kc and 10 kc to suppress 
low-frequency noise originating on the barge or in 
the water, and three high-frequency filters cutting 
off frequencies above 50, 70, and 120 kc and thus 
eliminating noise of radio origin. Components of these 
filters are shown in Figure 31 and the location of the 
rack-mounted assembly in Figure 17. 

10.7.5 Voltage Level Recorders 

Until early in 1944, the recorders used at the meas¬ 
uring stations were Type FR, manufactured by the 
Sound Apparatus Company of New York. This in¬ 
strument is designed to cover a voltage level range of 
40 db over a frequency range from 20 to 20,000 cycles. 
.A.S supplied by the manufacturer, its performance in 
the supersonic-frequency range leaves much to be 
desiredThe recording pen is coupled to a contact 
that moves over a logarithmic potentiometer in such 
a manner as to keep the power input to the recorder 
constant under varying applied voltages. The move¬ 
ment of the pen carriage is jjroduced by a magnetic 
clutch that couples the pen carriage to the proper 
side of a disk rotating at constant speed in a manner 
to maintain a constant input. The rotational speed 
of the wheel is such as to give a maximum sj^eed of 
pen motion of 40 db per second. For supersonic work 
the outstanding defects of the recorder in its original 
state were a marked decrease in response above 50 kc 
and erratic behavior of the magnetic clutch. Figure 
32 shows the circuit diagram of the recorder in its 
original form plus a stage of d-c amplification to in- 
crea.se the ratio of the d-c output voltage to the a-c 
input. 

The modified circuit .shown in Figure 33 represents 
contributions of the HUSL staff to the improved per¬ 
formance of this instrument in the desired frequency 
range. Thus modified and with a certain amount of 
nursing, it was used at Spy Pond with a rea.sonable 
degree of satisfaction. The coupling device to the 
200-D oscillator is shown in Figure 17. The gearbox is 
shown on the top of the recorder. It contains a gear 
train by means of which two ratios of oscillator speed 
to recorder-tape speed can be obtained. Samples of 
the recorder traces of the sound apparatus recorder 
trace have already been shown. 



Figure 34. Leeds & Northrup recorder mounted in rack. 


CONFIDENTIAL 








OPEN-WATKR MEASUREMENT AT IIUSE 


:m)8 


The Leeds & Northrup Speedomax power level re¬ 
corder used in the final installation at the barge is 
shown in Figure 34. Voltage levels are recorded on a 
tape 10 in. wide, covering a 40-db range of variation 
of the recorder input. It is designed to operate be¬ 
tween 150 and 150,000 cycles and over this range is 
accurate to 0.5 per cent of full .scale. The 0-decibel 
input level corresponds to a voltage of about 5 inv 
and can be adjusted over a range of approximately 
10 db about this value. The input impedance is ap¬ 
proximately 165 ohms. The speed of response of the 
recorder is such that the |)en will traverse any part 
of the 10-in. chart and arrive at complete balance, 
without overshooting, in approximately 1.5 .sec. The 



Fioure .3.i. Response c.alihration from L & X recorder. 


l)aper is dri\mn 6 in. per minute by a .synchronous 
motor. An extra pair of spiral gears is supplied with 
the accessories so that paper speeds of 3 in. per 
minute or 6 in. per hour may be obtained in place of 
the standard speed. A .switch permits “continuous” 
or “limited” paper drive; when it is on “limited,” the 
drive stops if the pointer reaches either extreme of 
the scale. The frecpiency marker pen at the left end 
of the chart is operated by the circuit shown in Fig¬ 
ure 20. The recorder itself operates from a standard 
115-volt 60-cycle supply. A respon.se curve and \ olt- 
age calibration curve are shown in Figure 35. 

10.8 PROJECTORS AND STANDARD 
HYDROPHONES 

10.8.1 Projectors 

Several projectors, both crystal and magnetostric- 
tive, have been used for measurements at the field 


stations. The first were the HUSL 1 X 1-in. X-cut 
Rochelle .salt crystal hydrophones made in the lab¬ 
oratory. The.se were quite similar in construction to 
the HK .series developed at the Ma.s.sachusetts Insti¬ 
tute of Technology.'-® The main point of difference l)e- 
tween the two was the substitution in the Harvard 
units of glass for the metal faces — and later rubber 
- of the MIT model. Units known as “Harvard 
6X6” projectors were built later. These were simi¬ 
lar in mechanical con.struction to the 1 X I’.s, with 
a 6 X 6-in. radiating surface divided into four quad¬ 
rants with connections for operating the quadrant 
in .series, parallel, or series-parallel. Driven at con¬ 
stant voltage, these units showed a rising frequency 
characteristic due to the drop in impedance with in¬ 
creasing frecpiency. 

Later, the Rrnsh Model C-1.3-2 X-cut crystal hy¬ 
drophone became standard ecpiipment at both sta¬ 
tions. This has a 4 X 4-in. radiating area of Rochelle 
salt crystals surfaced with a rubber face and mounted 
on heavy metal backing plate. For HUSL use, the 
front-to-back discrimination was increased by ce¬ 
menting a /<t-in. layer of corprene on the back sur¬ 
face. These units showed good patterns up to 80 kc, 
with the frequency response tyi)ical of crystal pro¬ 
jectors. The data for Figures 36 and 37 were supplied 
by the manufacturers, the Brush Development Com- 
jmny, Cleveland, Ohio. 



Figure 36. Transmitting resjjotise of Rru.sli C 13-2 
transducer. 


At freciuencies below 10 kc the crystal hydrophones 
gave relatively low outputs, with distorted wave 
forms. In this range, the Type IK low-frequency 
electrodynamic projector developed by the Bell Tele¬ 
phone Laboratories was used.^®The somewhat rag¬ 
ged frequency characteristic in the 6- to 10-kc 
range proved an objectionable feature of this pro¬ 
jector. The XPA 3 X 12-in. crystal unit developed 


CONFIDENTIAL 










































IMIOJECTORS AND STANDARD HYDROPHONES 


.{09 



Figurf, 37. Impedance characteristics of Itrush C 13-2 
transducer. 



X PA 
3" X 12" 
CRYSTAL 


HUSL 
I" X I" 
CRYSTAL 


BRUSH 
MODEL 
C - 13* 2 

a." 

CRYSTAL 


RING 

STACK 



Figure 30. QP projector. 


Figure 3S. Projectors used at field stations. 

l)y MIT -•'^proved more sati.sfaotory for low-frequency 
measurement.s. 

The temperature dependence of the X-cut crystal 
projectors, particularly when the water temperature 
approaches the Curie point of Rochelle .salt, is an in¬ 
herent defect of this type for measurement purposes. 
Magnetostrictive transducers, while relatively free 


from temperature effects, have low efficiency at fre¬ 
quencies far from resonance, but they have proved 
extremely useful in many types of measurement. Thus 
the B-19B’s, though designed jirimarily for use as 
hydrophones, have been used as projectors in the 
frequency range from 15 to 40 kc where fields of the 
order of 35 db vs 1 dyne per s(i cm at 2 meters ha^’e 
.sufficed. The B-19K (see Chapter 6, Section 6.3.2) 
has proved satisfactory for measurements between 5 


CONFIDENTIAL 






































































310 


OPEN-VS ATER MEASl KEMENT AT HI SE 




CHARACTERISTICS 
OF THE ABOVE 

network 

(Constant v input) 


/O 


IS 20 25 30 35 40 50 60 70 


Figure 40. Inverse network to give tint field with QP projector. 


and 10 kc. The thin-walled 60-kc ring .stack, less than 
a wave length in height (see Chapter 6, Section 6.4.6) 
has been used as a spherical source over the testing 
range from 10 to 70 kc. Some of the projectors men¬ 
tioned above are shown in Figure 38. 

The t)P projector (Figure 39), described in Chap¬ 
ter 6, Section 6.6, has proved more .satisfactory for 
most measurements in the range from 10 to 100 kc 
than any other projectors used. The average of 30 
mea.surements of field shown in Figure 41 was ob¬ 
tained with the compensating network shown in 
Figure 40 in.serted between the oscillator and the 
constant current amj^lifier. The constancy is shown 
by the maximum deviations from the aA'erage of 
these measurements made over a period of almost 
four months. 

10.8.2 Standard Hydrophones 

An ecpially diversified list of standard hydrophones 
has been used. The earliest standards used were the 
Bell Telephone Laboratories lA and 2A “square 
coil” pressure gradient hydrophones.'*' 

In a lA unit a rectangular coil is movable in the 
field of a permanent magnet. It has a fairly flat re¬ 
sponse from (). 1 to 50 kc, with a .sensitivity of approxi¬ 
mately —140 db vs 1 volt per dyne per sq cm and 
an impedance of about 60 ohms at 20 kc. The similar 


but smaller model, 2A,-- designed for use up to 100 kc, 
has an impedance of about 9 ohms at 20 kc and a 
.sensitivity of —152 to —162 db vs 1 volt per dyne 
per sq cm over the measuring frequency range. Be¬ 
cause of their low sensitivity and rather fragile con¬ 
struction, these hydrophones were not the ideal in¬ 
struments for many of the measurements required. 
The original calibrations were supplied by the Under¬ 
water Sound Reference Laboratories of Columbia 
University Division of War Research [USRLl. 

The development of the B-19B and later the B-19II 
hydrophones met the need for sturdier and more 
.sensitive standards. Reciprocity calibrations of .se¬ 
lected units of these types, which were found to check 
very clo.sely with USRL calibrations of similar units, 
gave reliable standards for field measurements for 
frecpiencies between 10 and 100 kc.'** 

.4. relatively .small proportion of the measurement." 
made at HUSL was in the range of audible fre- 
cpiencies. The standard hydrophones used were the 
3A and the 5E crystal hydrophones designed for 
NDRC by the Bell Telephone Laboratories. The.se 
were all crystal units with the irreamplifier incorpo¬ 
rated in the hydrophone housing. Descript ion and per¬ 
formance data are given in references '''and "^'-'and 
With all the.se crystal transducers a separate battery 
power .supply for the preamplifier must be provided. 
The battery box, which was designed as a special unit, 


CONFIDENTIAL 








































ABSOLUTE ClALIBRATION OF HYDROPHONES 


:ui 



Figure 41. Field of QP-1 with constant current amplifier and inverse network. 


is .shown in Figure 17 and the circuit in Figure 42. The 
unit i,s supplied with a meter for measuring filament 
and plate voltages and amphenol plugs to fit the 
terminals of the crystal hydrojihones. The 135-ohm 
resistor across the signal leads from the hydrophone 
provides the proper termination for the 5E pre¬ 
amplifier. 

The hydrophones mentioned in the foregoing para¬ 
graph are illustrated in Figure 43. 



Figure 42. Battery power .suiiply for standard crystal 
transducers. 


10.9 ABSOLUTE CALIBRATION OF 
HYDROPHONES 

The theory underlying the ab.solute calibration of 
a linear reversible transducer appears in Chapter 1. 
In making reciprocity calibrations at HUSL, the 


measurements were made in such a way that ccpia- 
tion (32) of Chapter 1 could be used in calculating 
the .sensitivity of the reversible transducer C, used 
both in transmission and recejition. To repeat equa¬ 
tion (32)^ of Chapter 1, 



Figure 43. Standard hydrophones used at HUSL. 


where J is the reciprocity parameter 2r/pf X 10“^ r 
being the constant distance between transmitter and 
receiver at which the three sets of voltage and cur- 


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312 


OPEN-WATER MEASUREMENT AT HUSL 


rent measurements show n in Figure 20 of Chapter 1 
were made and I the constant value of the trans¬ 
mitting current. Ei and are voltages generated in 
transducers B and C respecti\-ely by a current h = h 
in transducer A, while Ez is the voltage generated in 
B by the current I in transducer C. By reference to 
the right-hand member of the equation, it is ap¬ 
parent that the absolute value of the current in 
transducer -4 wFen Ei and E^ are being measured need 
not be known. It is only necessary that the current 
be the same in the two cases, since it is the ratio of 
Ei\o El that enters into the e.xpression and this ratio 
is independent of the magnitude of the driving cur¬ 
rent in transducer ^4. ^4 is used only as a transmitter 
and B only as a receiver, so that neither need be 
reciprocal. Transmitter C is used in both transmis¬ 
sion and reception and a linear relation must e.xist 
between current and generated [pressure and between 
pres.sure and voltage over the whole range covered in 
the measurements. A corollary of this last is the re¬ 
quirement that the acoustic output of C shall be un¬ 
distorted. 

The .sensitivity of a tran.sducer is recorded in deci¬ 
bels referred to 1 volt per dyne per s(iuarecm. With 
equation (1) put into logarithmic form, 

20 log Sc = 10 log J -f 10 log Ei 

+ 10 log Ez — 10 log Fi — 10 log I. (2) 

Since the voltages are recorded in decibels referred 
to 1 volt, (20 log E), logarithms of the FJ’s can be ob¬ 
tained by di\'iding the measured voltage levels by 2. 

The actual measurement procedure followed in 
making a reciprocity^ calibration may be illustrated 
by the calil>ration of a B-19 hydrophone. 

The Brush 4X4 was used as transducer A, a 
B-19H as transducer B, and the B-19B as transducer 
C. The flriving level of A was fixed by adjusting the 
gain of the driving amplifier to a given voltage at 
some definite frequency, in this case 10 volts at 10 kc. 
The respon.se of the B-19H placed at a definite point 
in the field was recorded. A calibrating voltage was 
injected from which the voltage level 20 log Ei could 
be measured. The B-19B was then put down in the 
same position as that occupied by the B-19H and, 
with the driving conditions unchanged, the voltage 
level 20 log Ei was measured. With the B-19B main¬ 
tained in its position, the Brush 4X4 was replaced 
by the B-19H. The B-19B was then driven, the 
driving current being kept at a constant value, which 
was measured by means of a Ballantine vacuum-tube 


voltmeter [VTVM] acro.ss a calibrated 1-ohm resistor 
inserted in the leads of the B-19B. The voltage level 
generated at the output of the B-19H is 20 log Ez, 
the value of which is determined from the response 
and calibration curves in the usual manner. The 
values obtained from measurements made in this 
manner can all be inserted in logarithmic form of the 
equation for the .sen.sitivity of the B-19B. (Half the 
voltage levels of Ei, Ei, and Ez must, of course, be 
used.) 

The reciprocity parameter ./ is a function of fre¬ 
quency and may be computed for each frequency. 
A preferable procedure, however, is to reduce the 
expression for J to the logarithmic form 

10 log ./ = 10 (log 2 -f- log r — log p — log/ — 7) 

= 10 log r — 10 log / — 66.9. (3) 

Tables of values of 10 log ./ for the needed values of 
r and / may be prepared. A simpler procedure, how¬ 
ever, is to plot on semilog paper 10 log J as a function 
of / with r as a jiarameter, r being measured in centi¬ 
meters, since the density of water is taken as 1 gm 
per cubic cm. So plotted, 10 log ./ appears as a family 
of parallel straight lines from which its vxilue for any 
given values of r and f can be taken. 

The sensitivity of the reciprocal transducer having 
been determined, the .sensitivity of transducer B can 
be deduced by direct comparison of the measured 
\’oltage levels of Ei and Ei, .since both were generated 
by the same sound field. The sensitivity of trans¬ 
ducer *4, however, cannot be derived from the mea.s- 
urements described. 

10.9.1 Results of Reciprocity 
Calibrations 

(Mea.surements for the first absolute calibration of 
a tran.sducer at HUSL were made on April 20, 1943, 
on a laminated .stack tran.sducer, HP-4. The re.sults 
of those measurements were u.sed to evaluate the 
sensitivity of the HP-4 and also to check the calibra¬ 
tion of the BTL standard L\ No. 17 supplied with the 
instrument.” 

The .sensitivity of the latter as deduced from the 
measurements agreed to within 1 db with the values 
given by BTL over the frequency range from 10 to 
40 kc. From 40 to 70 kc, differences were no greater 
than 3 db. 

Since that date, refinements in measuring tech¬ 
nique have been made, with periodic checks of the 


CONFIDENTIAL 



AUXILIARY MEASURING EQUIPMENT 




various standards used at the field stations. In most 
of these, a Ballantine VTVM has been used for re¬ 
sponse and voltage calibration in place of the level 
recorder. The degree of reproducibility in the results 


T.\Br.E 1. Absolute sensitivity of B-19B, in db vs 
1 volt per dyne/sq cm. Average from 13 reciprocities. 


Freq. 
in kc 

Sensitivity 

Deviation 
from Ebaugh 

0.675 of 

rms error 

7 

- 117.4 

- 0.2 

0.7 

8 

- 115.0 

+ 1.0 

0.9 

9 

- 114.4 

-1- 0.2 

0.2 

10 

- 115.2 

4- 0.1 

0.4 

11 

- 11.5.0 

+ 0.3 

0.5 

12 

- 114.1 

+ 0.3 

0.6 

13 

- 113.2 

+ 0.3 

0.6 

14 

- 115.1 

0 

0.5 

15 

- 113.3 

+ 0.3 

0.5 

16 

- 113.3 

-h 0.2 

0.4 

17 

- 112.8 

-b 0.1 

0.3 

18 

- 112.6 

- 0.1 

0.5 

19 

- 113.3 

- 0.2 

0.5 

20 

- 113.9 

- 0.4 

0.5 

21 

- 113.4 

-b 0.2 

0.4 

22 

- 112.4 

+ 0.1 

0.3 

23 

- 111.6 

0 

0.2 

24 

- 111.3 

- 0.3 

0.4 

25 

- 111.9 

0 

0.5 

26 

- 111.3 

- 0.1 

0.4 

27 

- 111.8 

+ 0.3 

0.5 

28 

- 112.7 

- 0.2 

0.7 

29 

- 113.3 

+ 0.5 

0.4 

30 

- 113.2 

+ 0.7 

0.5 

32 

- 112.0 

- 0.1 

0.7 

32.2 

- 116.4 


0.8 

34 

- 112.8 

- 0.3 

0.5 

36 

- 112.7 

- 0.4 

0.3 

38 

- 113.1 

- 0.4 

0.3 

40 

- 112.9 

- 0.2 

0.2 

42 

- 113.2 

- 0.2 

0.2 

44 

- 113.5 

— 0.5 

0.3 

46 

- 113.6 

- 0.3 

0.4 

48 

- 113.5 

- 0.5 

0.4 

50 

- 113.6 

- 0.3 

0.5 

52 

- 113.4 

- 0.4 

0.5 

54 

- 113.7 

- 0.7 

0.7 

56 

- 113.5 

- 0.6 

0.6 

58 

- 112.8 

- 0.6 

0.5 

60 

- 113.3 

- 0.5 

0.5 

62 

- 114.0 

- 0.6 

0.5 

64 

- 114.4 

- 0.7 

0.5 

66 

- 114.5 

- 0.4 

0.5 

68 

- 114.8 

- 0.5 

0.5 

70 

- 115.1 

- 0.6 

0.6 


of such measurements can be inferred from Table 1. 
A careful analysis of the data from a large number of 
measurements indicates that fluctuations in the sound 
field between the .source and the receiver constitute 
the chief source of error in single measurements.-^* 
The individual calibrations, which are averaged in 
Table 1, were made with considerable care, so that 


the precision there shown should naturally be greater 
than might be expected in routine measurements. 
From the same analysis it was concluded that 95 to 
98 per cent of single measurements made under rou¬ 
tine conditions would fall within a range of ± 1.5 db 
from the statistical mean of a number of measure¬ 
ments made under carefully controlled conditions.” 


10.10 AIXILIARY MEA.SIIRI\G 
EQUIP.MENT 

10.10.1 Current Supply for 

D-C Polarization 

To provide means for introducing direct current 
into the windings of transducers requiring d-c polari¬ 
zation, a storage battery with charger was installed 
in both the barge and Spy Pond laboratories. The 
front of the battery box, on which were mounted 
meters, switches, and rheostat controls, is shown in 
Figure 17. 

Eighteen 6-volt storage batteries, housed in a 
wooden box with three shelves, provided a direct- 
current source for operation of d-c motors, polariza¬ 
tion of transducers, and numerous other uses. Two 
batteries were connected in series, each pair being 
wired to Giant insulated jacks mounted on a Transite 
.switching panel on the front of the battery box. 
Therefore, each pair of jacks on the front panel sup¬ 
plied 12 volts. .\ny combination of the 12-volt .sec¬ 
tions could be connected to the output circuit by 
plug connectors, thus providing a means for con¬ 
trolling the current output of the battery up to a 
maximum value of 25 amp. The output was wired 
directly to d-c input terminals on the impedance¬ 
measuring and d-c polarizing panels. A General 
Electric Tungar battery charger, capable of charging 
any combination up to 12 batteries, was mounted on 
top of the battery box and wired to the Giant in¬ 
sulated jacks on the Tran.site panel. 

10.10.2 Polarizing-Current and 
Impedance-Measuring Panels 

At Spy Pond, a special panel was installed which 
served a dual purpose of introducing polarizing cur¬ 
rent into a transducer in the water and/or providing 
means for making impedance measurements on a 
transducer in the water. The wiring diagram is shown 


CONFIDENTIAL 















314 


OPEN-WATER MEASUREMENT AT HUSL 


MALLORY 4 POS 
4 SECTION 




Figure 45. Circuit for impedance mea.surement.R. 


the line leading to the battery supply. When it is 
desirable, a toggle switch opens the low side of the 
line leading to the battery supply. When polarizing 
current is used in a transducer acting as either a pro¬ 
jector or a receiver, the conden.ser switch is thrown 
to the l-/if position on the high side of the cable lead¬ 
ing to the power amplifier or receiving amplifier, 
thus keeping the polarizing current out of the input 
transformers. In either straight receiving or trans¬ 
mitting tests, the .series re.sistor .selector .switch is 
thrown to the “.short” position. 

With a .single-section (two-terminal) tran.sducer, 
the only requirement on the choke besides its ability 
to carry the direct current is that the a-c power di.s- 
sipated in it be small in compari.son with that de¬ 
livered to the tran.sducer. With multiple section 
transducers there is the additional requirement that 
coupling introduced between sections by the polariz¬ 
ing circuits be .small. The latter requirement is met 
by .suitable placement of the circuit elements. 

When the conden.ser switch is thrown to the CiR 
decade condenser and a 1-, 10- or 100-ohm resistor is 
introduced in .series, it is possible to obtain voltage. 



in Figure 44. Two chokes prevent a-c power from 
being dissipated in the battery supply. These chokes 
have an inductance of 230 mh; a Q of 8, measured 
at 1 kc; and a d-c resistance of 6.2 ohms. A four- 
position four-gang switch introduces a single choke 
or both chokes in parallel, shorts them out, or opens 


current, and .series-tuning capacity data for use in 
computing the impedance of the transducer as well 
as the power input. This circuit through the panel 
is repre.sented in Figure 45. The polarizing circuit is 
not shown here, but it can be used, if nece.ssary, with¬ 
out serious alterations of the values obtained. 


CONFIDENTIAL 


































































































AUXILIARY MEASURING EQUIPMENT 


313 


2051 6AC7 6L6 



ators were built for this use. The one shown in Figure 
46 gave two narrow band outputs, from 15 to 30 and 
55 to 75 ke, and a third wide band from 15 to 75 kc. 

The generator shown in Figure 47 was designed to 
give two bands centering at 24.5 kc and at 60 kc, 
frequencies on which interest was particularly cen¬ 
tered. 

10 . 10 . t Analyzer for Noise 
Measurements 

iSIost test.s involving noi.se measurements were 
made with the analyzer, the circuit for which is shown 
in Figure 48. Any noise or pure-tone signal voltage 
appearing acro.ss the input terminals is heterodyned 
with a pure-tone signal from a local o.scillator, the 
difference \mltage from the mixer tube being ampli¬ 
fied and passed through a low-pa.ss filter to the out¬ 
put. The pass band of the analyzer .simulated that 
in the receiving circuit of the tran.sducer under study 
and thus j^rovided a means of measuring hydrophone 
resjionse to noise under the same conditions as those 
under which the hydrophone would be operated in 
practice. Since the i)ass band of the analyzer (1,960 
cycles) was known, the results of mea.surements 
through the analyzer could be evaluated in terms 



10.10.3 Noise Generators 

Certain types of mea.surements at Spy Pond called 
for knowledge of the response of transducers to noise 
lying within a specified frequency band. Two gener- 


of “spectral .sensitivity,” that is, the sen.sitivity to 
continuous spectrum noise, referred to a band width 
of one cycle and to a pre.s.sure of 0.0002 dyne per 
.'^q cm. 

Several changes in the analyzer increased its use- 


CONFIDENTIAL 





























































































































.{16 


OPEN-W ATER AIEASLKEMENT AT HUSL 


I KC OUTPUT 



fulness. Two coils and a band selector switch added 
to the local oscillator made possible the covering; and 
selection of the frequency ranges of 4.2-7.0 kc, 18.3- 
33.3 kc, or 31.0-71.5 kc. A greater frecpiency range 
was covered by substituting a Hewlett-Packard oscil¬ 
lator for the local oscillator. This substitution was 
effected by connecting the Hewlett-Packard o.scillator 
to GR terminals added to the analyzer and replacing 
the 6SN7 by a similar tube, with the pin connections 
for the o.scillator section removed. 

10.10..5 Frequency Standard 

While the frecpiency scales of the oscillator used 
were sufficiently accurate for many measurements, 
occasional discrepancies appeared, because of the 
drift of the oscillator from calibration. A bimetal 
temperature-compensated tuning fork manufactured 
by the Riverbank Laboratories, Geneva, Illinois, pro¬ 
vided a stable 1,000-cycle standard frequency.^* This 
fork was used as the frequency-controlling element 
in the o.scillator circuit comsisting of the 6SG7 and 


6SX7 stages shown in Figure 49. The diode-con¬ 
nected half of the 6SX7 is used to provide an auto¬ 
matic volume control [AVC] bias to the 6SG7 ampli¬ 
fier. This AVC is neces.sary because the initial gain 
required to insure that the fork be self-starting is 
higher than the gain necessary to maintain oscilla¬ 
tions of the fork at the optimum amplitude for good 
stability and wave form. 

The oscillatory frequency could be checked against 
the output of the tuning-fork oscillator at any multi¬ 
ple of 1 kc by means of Lissajous figures on an oscillo¬ 
scope. However, the identification of the frequency 
of the higher harmonics by means of the Lissajous 
pattern is difficult. By using harmonics of the 1-kc 
oscillator, higher frequencies can readily be obtained. 

The harmonic generator consisted of a 6H6 recti¬ 
fier and a 6SJ7, so biased that it was driven to cutoff, 
producing an approximately square wave that, when 
differentiated, gave positive and negative pulses 
spaced at 500-cycle intervals. Either the positive or 
negative inilses were then rectified and the remaining 
pulses used to shock-excite a tuned circuit, which 


COXFIDEXTIAL 























































































AUXILIARY MEASURING EQUIPMENT 


317 


was part of ao oscillator that contained enough feed¬ 
back to keep it from oscillating. The purpose of the 
tube (J46SN7) was to improve the Q of the tuned 
circuit by introducing a negative resistance into it. 
This high Q circuit oscillated only at harmonics of 
the jiulsing frequency when sufficient feedback was 
pre.sent to keep it from oscillating by itself. Its output 
was fed to a cathode follower to Isolate the circuit 
and give a low impedance output for the device. The 
tuned circuit consisted of a three-section variable 
conden.ser, 150 per section, with the sections in 
parallel and a Bell Telephone Laboratories toroidal 
coil with molybdenum-Permalloy core, having an in¬ 
ductance of 450 mh and a Q of appro.ximately 80. This 
combination gave outputs from 7 to 14 kc with only 
the harmonics of 1,000 cycles appearing. The unit 
delivered 734 volts at 1 kc and from 7 to 3 volts from 
the harmonic generator, depending on the setting of 
the feedback potentiometer. 

The unit was calibrated against Harvard’s Cruft 
Lal)oratory 1,000-cycle standard throughout several 
eight-hour continuous running periods. The fre- 
(piency did not vary perceptibty. The fork was 0.1 
cycle below the Cruft Laboratory standard at 1,000 
cycles. 

10.10.6 Portalile Polar Chart Recorder 

Some use has been made of a direction pattern tracer 
(portable polar chart recorder [PPCR]) designed in the 
laboratory.This device plots directional patterns 
on polar-coordinate paper. A gear mounted on the 
shaft rotating the transducer drives a CT synchro¬ 
motor which in turn controls a .second C’T .synchro¬ 
motor within the recorder. The recorder motor con¬ 
trols a .servomotor that drives the recorder turntable 
in synchronism with the rotating shaft. The elec¬ 
tronic part of the recorder consists of a cathode-fol¬ 
lower input followed by a low-impedance logarithmic 
attenuator, the output of which feeds into an ampli¬ 
fier, followed by a rectifier and differencing circuit 
to obtain a d-c output. The d-c output is modulated 
with 60 cycles and the result is amplified and fed to 
a 60-cycle motor that drives the recorder pen. 

10.10.7 Four-Channel Amplifier 

Some of the measurement work at Spy Pond called 
for the comparison of four hydrophones mounted in 
a single cylindrical body. To in.sure identical condi¬ 
tions for both the acou.stic signal applied to each of 


the transducers and the electric output to the meas¬ 
uring amplifier, it was desirable to make the measure¬ 
ment on each hydrophone in turn without the time- 
consuming job of removing the body from the water 
and opening it. A further desideratum was to make 
the mea.surements at the output panel of the pre¬ 
amplifier, located within the submerged body, and 
thus eliminated the effect of the twenty feet of cable 
needed for connection to the regular receiving ampli¬ 
fier. The conditions of measurement thus became 
identical with those that would prevail in the actual 
operation of the tran.sducers. Figure 50 shows the 
amplifier with the four preamplifier circuits designed 
and built for this jmrpose. The power supply was 
contained in a separate cha.ssis mounted in the relay 
racks. The final amplifier with .switching control for 
the channels was also built in a .separate chassis 
mounted in the racks. The four-channel preamidifier 
was contained in a boxlike chassis placed inside the 
cylindrical body in which the hydrophones were 
mounted. Connection from the preamplifier to the 
main amplifier was through three braided six-wire 
shielded cables about 20 ft long which passed through 
water seals in the back plate of the cylinder. With 
this combination it was possible to calibrate four 
.separate hydrophones without taking off the back- 
plate to change from one hydrophone to another. A 
switch on the amplifier panel controlled three relays 
in the preamplifier so that any one of the four hydro¬ 
phones and preamplifier tubes could be .^witched into 
the d-c cathode-follower output channel of the pre¬ 
amplifier. 

10.10.8 Special Apparatus for 
jMeasurenients on 
IMultielenient Transducers 

In addition to the apparatus already described as 
standard equipment of the field stations, a portable 
impedance bridge (see Chapter 9) was required. The 
measurement of the phase relations of the responses 
of the different transducer elements to the incident 
sound called for a specially designed phasemeter, 
which consisted essentially of twin channels, each of 
which comprised the following elements. (1) A phase 
inverter, with a two-position switch, allowed the 
transmi.ssion of the signal with phase inverted or un¬ 
inverted as desired. (2) A series of amplifying tubes 
terminated in a twin diode clipped both halves of the 
incoming sine waves. These diodes were bia.sed so 
that they clipped when the amplitude of the amplified 


CONFIDENTIAL 



318 


OPEN-WATER MEASUREMENT AT IIUSl 



CXJNFIDENTIAL 


Figure 50. Foiir-cliiuiiiel amplifier used at Spy Pond. 























































































































































































SPECIAL TESTS: CALIBRATION OF SOUND GEAR MONITOR 


319 



signal exceeded 1.5 volts. Amplifying and cliijping 
were repeated until the wave form was approximately 
“square.” (3) A differentiator using a conventional 
RC circuit gave a series of pulses, one at each crossing 
of the voltage axis by the original sine wave. These 
pulses were passed through a two-stage pulse ampli¬ 
fier, the last stage of which clipped off the positive 
pulse, leaving the negative pulse to excite the sup¬ 
pressor grid of the tube in the trigger circuit. Shown 


BALLANTINE 
LEVEL METER 



BALLANTINE 
LEVEL METER 


Figure 52. Block diapiram illustrating phase-difference 
mea.surements. 


in Figure 51 is a block diagram of the circuit just 
described, together with a wiring diagram of the 
trigger circuit, by which phase differences in the sig¬ 
nals received at the inputs of the two channels were 
indicated on a zero-center d-c meter. 

As designed, the pha.semeter required between 0.4 
and 1.2 volts input, which for most measurements 
required amplification of the signals from the trans¬ 
ducer elements. A two-channel amplifier designed to 
give identical pha.se shifts in the two channels was 
built for this purpose. The usual arrangement for 
measuring pha.se differences between the outputs of 
individual elements is shown in Figure 52. It will be 
noted that in this arrangement the phasemeter is used 
simply as a null indicator. The setting of the standard 
lag line needed to give a null indication gives the 
phase difference between the outputs of the two ele¬ 
ments. 

10.11 SPECIAL TESTS: CALIBRATION 
OF SOUND GEAR MONITOR 

A wide variety of special tests was required from 
time to time during the life of the field stations. Gen¬ 
erally these could be carried on with unprovlsed gear 
supplementing the standard equipment already de¬ 
scribed. One of the more important routine jobs was 
the calibration of the sound gear monitor [SGM]. 

A large number of preproduction units of this de- 


GONFIDENTIAL 





































































OPEN-WATER MEASUREMENT AT HUSL 


.•{2() 


DATA SHEET FOR S.G.M 

DEPTH. V, . 

DISTANCE . 

MEAS. HYDROPHONE.. 

SOURCE .VT.-/. .VOLTAGE . AT 10 kc 


ASSEMBLY MEASUREMENTS 

DATE.. 

OBSERVERS. ‘2'“, : 

CHASSIS. SC 
HYDROPHONE . 3 


FIELD MEASUREMENTS 


FREQUENCY 

17 

1 8 

19 

20 

21 

2 2 

23 

24 

25 

26 

1. Response of standord 
(Aft : 30 T-3P ijb 

-16 



-16 

-163. 

-13.7 

-/39 

70.7 

-//./ 

-7.r 

Colibrotion 

( -€)0 db vs. 1 volt) 

-9.7 

-7.P 

-9.9 

-/ao 

-/0.Z 

-{0.(5 


-{0.0 

-9.P 

-9.S 

«• 

Voltage response 











* 

Sens, of Standard 











Field db vs. 1 bar 


77 

70> 

-1 

7^ 

vg 

50 

7?.3 

5-/. 5 

50.5 

1 

53 

S.G.M. Receiving 60' cable 

Vo 

70 

70 

7o 

7o 

7o 

7o 

7o 

70 

7o 

a. "Read direct" 

-9 

-io.9 

-7.7 

-6.7 

-5.? 

-5.0 

-3.3 

-f3.7 

-/.(o 

-5 

b "Subtract 30" 

6>r 

-3.0. 

(or 

7 

-3.0 

(^7 

-/.? 

67 

-/ 

67 

-0.3 

■(■ /.o 

7o 

-A 3 

7o 

—C. S- 

70 

-j.r 

c. Same as (b) with 




67 



<c7 



70 

75' extension 

-3.U> 



-3.0 






-7.0 


S.G.M. Sending. Meosuring hydrophone receiving. Attenuation some as in 
meosuring field. 


Response full volume 
(Attenuation. db 

-3/ 


-33. S' 

- 33.5 

-3/ 

-3./ 


-/75 

-/r 

-( 7.5 

Response 10 db in 

_ 

-J-Z 

_ 

-3 / 




^5 

1 

-3^.5 

-355 

-37 

-37 


Moy be computed later 

Figure 53. Data sheet for SGM calibration. 


vice were l^uilt at HUSL. In addition, the laboratory 
was called upon for [iroduction tests of selected units 
supplied by outside manufacturers. An outline of the 
procedure followed in the calibration of these instru¬ 
ments is giiven here. 

A B-19B hydrophone is used (1) to set uj) a .sound 
field of known intensity at a specified tlistance in the 
water and (2) to receive the acoustic .signal from 
sound gear under test.'^ 

The SUM comprises a transmitting oscillator to 


cover the frequency range from 17 to 26 kc and a re¬ 
ceiving amplifier with an attenuator meter and a 
meter graduated in decibels to indicate the pressure 
level of the received signal. These are carried in a 
metal box with externally mounted frecpiency dial 
and attenuator knobs. One of the two attenuators in 
the recei\-ing circuit is a 30-db pad. The other is a 
40-db potentiometer, variable in steps of 2 db. 

The calibration of the SGAI consisted of two steps: 
a calibration of its receiving .system so that it could 


CONFIDENTIAL 














































































INCIDENTAL STUI>Ii:S 


:I21 


he used as a direct reading instrument for the meas¬ 
urement of sound-pressure level, and a measurement 
of the sound-ijressure level developed by the trans¬ 
mitting section of the unit at a given distance from 
the B-19B hydrophone. The procedure followed is 
indicated in outline form in the headings on the data 
sheet shown in Figure 53 . 

For the check on receiving characteristics, a jmre 
tone field was set up and measured by a standard 
hydrophone at a distance of 5 ft. The Ballantine 
VT\'M (decibel scale) was used as the measuring 
instrument. The field was measured at 1,000-cycle 
intervals over the 17- to 26-kc range. The standard 
was then replaced by the B-19B hydrophone of the 
sound gear monitor. No special precautions were 
taken to orient this B-19B, since its horizontal pat¬ 
tern is flat in the frequency range used. The settings 
of the 40-db attenuator on the monitor with the 
30-db pad out and the meter reading at each fre¬ 
quency were recorded. As a check on the 30-db pad, 
the readings were repeated with tins attenuator in¬ 
serted. A check on the 75-ft extension cable used with 
the tran.sducer was made by connecting the cable 
and repeating the last set of measurements at four 
frequencies. 

For the check on transmitting behavior, the SGM 
control switch was changed over to the “send” po.si- 
tion in which the standard hydrophone is used as the 
receiver. It was aligned acoustically and set at ex¬ 
actly 5 ft from the monitor transducer. The output of 
the standard was fed into the same receiving channel 
used in measuring the field, with the same attenu¬ 
ation in the measuring amplifier to avoid the neces- 
.sity of repeating the voltage calibration. As a check 
on the 10 -dl) pad, the same set of readings was re¬ 
peated with this attenuation added. 

The pressure level corresponding to the lowest 
attenuator setting and to the zero meter reading 
could be computed for each frequency from the 
attenuator setting and meter reading when receiving 
and from the measured values of the field. These com¬ 
puted values constituted a calibration of the 8 ( 1 M as 
a .sound level meter. Comparison of the respon.se of 
the standard to the measured field with its response 
to the field generated by the monitor in the “.send” 
position gave the value of the field set up by the 
monitor at 5 ft. 

10.12 INCIDENTAL STUDIES 

During the course of the work directed specifically 
to the study of tran.sducer characteristics, .some sig¬ 


nificant data were obtained on water conditions as 
they affect acoustic measurements. 

10.12.1 IMeasurement of Velocity 

of Sound 

A fairly precise direct measurement of the velocity 
of .sound in water was made using the pha.se-mea.sur- 
ing apparatus previously described. The phase differ¬ 
ence <t> between the output signals of two similar 
hydrophones is given in degrees l)y the equation, 

_ _ 360;/ 

~ c ’ 

whence 

df 

c = 360r—, 

(■/</) 

where r is the difference in path length of the sound 
arriving at the two tran.sducers. Thus, with two cali¬ 
brated B-19B hydrophones mounted on a fixed sup¬ 
port and so oriented that one was directly behind the 
other on the principal axis of the projector, the follow¬ 
ing measured values were obtained. 

Water temperature = 0.5 C 

Distance between hydrophones r = 22 .S in. 

df = frequency difference = 24,000 cycles per .sec. 

(}<t> = 3464 degrees 

24,000 

c = 360 X 22.8 X 7 ;- = 56,580 m. per sec. 

3,464 

= 1,444 meters per sec. 

The phase difference was determined by taking the 
cumulative value of the ob.served phase changes at 
5-kc intervals from 16 to 40 kc. 

10.12.2 Fluctuations in the Acoustic 

Field 

Fluctuations in the .sound field have already been 
mentioned as a source of measurement error. Refer¬ 
ence is made here only to those random variations, 
sometimes as great as ± 2 db Avithin a period of a few 
.seconds, that were observed at various times at both 
the barge and Spy Pond. The magnitude of the 
fluctuations was seen to increa.se with increasing 
distance between projector and receiver and in gen¬ 
eral to be less with transducers having a large area of 
radiating .surface than with small transducers. The 
spring and fall .sea.son.s were periods when bad days 


CONFIDENTIAL 






322 


OPEN-WATER MEASUREMENT AT IIUSL 


were most frequent, t)ut in midwinter and in summer 
smaller changes were common. They were of the 
order of +0.2 db and extended over a period of ten 
minutes or so. 

For a time, the fluctuations were thought to be 
due to the presence of fish, lured into the .sound field 
by the siren voice of the supersonic projector. This 
explanation was eliminated by illuminating the space 
l)etween projector and receiver and noting the fluctu¬ 
ations when no fish were pre.sent. Careful checking 
of the electronic gear ruled out instability there as a 
po.ssible explanation. Similar fluctuations were ob¬ 
served at the Sweetwater Station of the San Diego 
Laboratory. 

An unstable state of thermal equilibrium in the 
water at levels below the level of the projector and 
receiver has been confirmed as a cause of fluctuations 
by bathythermograph measurement at Spy Pond on 


days of severe field fluctuations. Temperature vari¬ 
ations as great as 8 F per foot change of depth have 
been noted. A partial remedy was the use of pressure- 
release screens. The screens first used at HUSL were 
of J^-in. Celotex encased in thin sheet metal. An 
improved screen was of solid sheet metal .surfaced on 
both sides with M-in. air-cell neoprene. Various ar¬ 
rangements of the screens were tried and found more 
or less effective, depending on the particular water 
conditions. The lowering of an inverted V-shaped 
screen proved effective in some instances. The .screen 
consisted of two .sections, each 2 ft by 4 ft, hinged 
along a long edge, and locked at an angle of 90 de¬ 
grees. Another arrangement that could be used in 
certain types of measurements consisted of two flat 
screens placed one above the other in the .sound field 
and .separated from each other to form a horizontal 
collimating slit. 


CONFIDENTIAL 



Chapter 11 


MAGNETOSTRICTIVE TRANSDUCERS 


HIGH POWER DRIVING OF 

11.1 INTRODUCTION 

11.1.1 Statement and Diseussion 

of Problem 

In many applications of magnetostrictive trans¬ 
ducers, the level of operation is low enough to make 
the performance of the transducer closely linear. 
Such an assumjjtion underlies the greater part of this 
hook. In particular, there are linear ecjuations (17) 
of Chapter 2, and (10), (11), and (13) of Chapter 3 on 
which this analysis has heretofore been based. Such 
analysis of operation has been found to be useful even 
when the basic linear ec}uations are known to be 
badly in error. This apparent validity of the linear 
theory .stems from the fact that usefid, efficient mag- 
neto.strictive transducers are operated at frequencies 
of mechanical resonance, and, therefore, the me¬ 
chanical vibration will be largely that of the funda¬ 
mental, even though the magnetostrictive forces 
contain ajipreciable second and higher harmonics. 
Similarly, the efficiency will remain nearly constant 
as the level is raised far beyond the point at which 
equations for the fundamental fail. 

When a transducer is operated at a rather high 
power level in an effort to make use of its full acoustic 
capabilities, nonlinearity will become very evident 
and must be taken into account. There are two 
places where nonlinearities enter. The first is in mag¬ 
netic behavior. Where previously proportionality was 
as.sured between increments in B and in H, with a 
constant proportionality factor /x, it will now be 
necessary to utilize the actual magnetization curve 
for this relation. The second departure from linearity 
concerns the magnetostrictive constant X. At high 
levels the magnetostrictive stre.ss that was previ¬ 
ously written — 'kB is no longer proportional to B. In 
equation (9) of Chapter 3 this stress is given as — ei?-, 
which implies that the value of X measured at low 
level is proportional to the polarizing induction. As 
shown in Chapter 4, this is true for nickel although 
apparently not for 2V-Permendur. 

Any analysis taking into account this nonlinearity 


is necessarily much more complex and involved than 
the linear theory. For example, since the magnetiza¬ 
tion curve is not approximated l)y any simple analyt¬ 
ical function, most calculations must be developed 
grc.phically or numerically. In the nonlinear case, it 
is necessary to specialize to a definite magnetic cycle 
and magnetization curve, .so that the results that 
can be obtained without very elaborate calculations 
are limited. Hence the experimental approach, using 
a certain amount of theoretical analy.sis as a guide, 
appears the best method of attacking the problem. 
The most important overall quantities to determine 
are the acoustic power output at the desired fre- 
cpiency and the electric power input. The idea of 
impedance loses much of its meaning when the trans¬ 
ducer is operated at high power, since voltage and 
current are no longer proportional and do not have 
the same wave form. However, the ratio of the funda¬ 
mental components of voltage and current may still 
be determined under specified conditions of opera¬ 
tion. Such information may be used to determine the 
proper matching network for the efficient transfer 
of electric power to the tran.sducer and to analyze 
the various loss components at the fundamental 
frecpiency. 

The problem of dynamic magnetostriction is analo¬ 
gous to many other physical problems in which ana¬ 
lytical theory has been usefidly worked out only for 
small variations of the parameters. As these vari¬ 
ations become large, the nonlinearities so complicate 
the analysis as to render quantitative development 
useless. In several such cases graphical presentation 
of experimental data has served to point the way 
toward the best operation of the device in regions 
where the nonlinearities make analysis impractical. 
The so-called contour charts of Chaffee ’■* have been 
useful in specifying optimum parameters for opera¬ 
tion of triode power oscillators and amplifiers. H. 
Chang and E. L. Chaffee extended the method to 
the steady-state operation of a magnetron o.scillating 
in its negative resistance mode. It is believed that 
conditions for optimum power conversion by mag¬ 
netostrictive devices operating in the nonlinear region 


CONFIDENTIAL 


323 


324 


HIGH POWER DRIVING OF MAGNP:T0STRICTIVE TRANSDUCERS 


may best be presented through similar graphical 
means. At present, low-level operation may be ade¬ 
quately predicted from vector or motional impedance 
loci. No extension of this method to prediction of 
operation at high levels is known to have been 
proposed. An exploratory investigation of the change 
with power level in the low-level vector impedance 
loci has been carried out. It will be pre.sented even 
though it differs widely in character from other 
successful grajdiical analy.ses of nonlinear data. 

The work reported in this chapter was initially 
directed to the determination of the power-handling 
capacity of a particular tran.sducer, on which no data 
were available. Experiment revealed the wide vari¬ 
ation in the characteristics of a magnetostrictive 
transducer with variation in the driving level. The 
initial attack led only to results applicable to the 
transducer under investigation. As the work pro- 
gre.ssed, the de.sirability of a more fundamental ap¬ 
proach appeared. The following questions became 
important. What, for example, is the upper limit of 
the electric power that can be converted into acoustic 
power per unit weight or volume? What are the 
merits of magnetostrictive as compared with electro- 
strictive materials in this respect? What is the effi¬ 
ciency of conversion of electric to acoustic power as 
a function of the level at which the conversion takes 
l^lace? The answers to these questions are obviously 
very u.seful when the size and weight of the trans¬ 
ducer and the power available enter into the design 
problem. 

The program of research was carried on with this 
broader purpose in mind. Definite and final answers 
have not been found to any of the foregoing ques¬ 
tions. The data presented, it is hoped, will l)e valuable 
as the ba.sis for a more conclusive investigation of a 
problem involving a considerable number of vari¬ 
ables with complex interrelations. 


11.2 CAVITATION 

Cavitation is a phenomenon which imposes aunique 
upper limit to the acoustic intensity that can be 
established in a liquid medium. Although cavitation 
is not specifically related to the properties of the 
transducer, it is an important factor in determining 
the performance limits of high-powered transducers 
for .sound generation in liquids. No .systematic in¬ 
vestigations of cavitation were carried out at the 
Harvard Underwater Sound Laboratory [HUSL^. 


Some work on the general prol)lem was done at the 
San Diego Laboratory, l)ut most of the information 
on this .subject is ba.sed on a continuing investigation 
carried out by Bell Telephone Laboratories under a 
Navy development contract. 

Definitive re.sults on the occurrence of cavitation 
are difficult to obtain, since ob.scure small-scale 
phenomena seem capable of exerting considerable 
influence on the on.set of cavitation. Tentative re¬ 
sults ba.sed on the Bell Telephone Loboratories’ work 
may be summarized as follows. 

In general, steady-state cavitation occurs in sea 
water or light liquids containing dissolved air or gas 
when the negative pha.se of the .sound-pressure wave 
reaches 1 atm. Increased hydrostatic pressure 
throughout the liquid produces a corresponding in¬ 
crease in the .«ound pressure at which cavitation first 
occurs. Removal of dissolved gases increases the 
.sound pre.ssure required to produce cavitation, indi¬ 
cating that different liquids display in varying de¬ 
grees an ability to .support tension under dynamic 
conditions. Heavy viscous liquids will usually support 
higher sound intensities without cavitation than light 
liquids, and degas.sed “bd” (bone-dry) castor oil 
permits higher steady-state sound intensity than 
other liquids so far investigated. 

Experiments indicate that sound pressures higher 
than steady-state values may be established without 
cavitation for short-duration pulses, and that the 
allowal)le power level increases as the pulse duration 
decreases. Numerical values characterizing this 
phenomenon are influenced by experimental details 
involving dega.ssing of the liquid, adsorption of gas 
on the tran.sducer face, temperature, geometrical de¬ 
tails of the transducer, and probably by other vari¬ 
ables. The data presented in Figures lA and B (from 
BTL) show spot values obtained with certain small 
tran.sducer models. The validity of the.se tentative 
clata in prediction of the performance of full-scale 
transducers under pulsing conditions has not been 
experimentally verified and the information should 
therefore be used with caution. 

It appears .safe to conclude, however, that short- 
pulse techniques offer the possibility of radiating 
much higher specific acoustic power into water or 
other liquids than had hitherto been thought possible. 
A considerable effort would seem to be justified in 
determining the influence of these considerations on 
the design of tran.sducers for high-level operation and 
in further iin-estigation of the basic j)hysical factors 
that control the on.set of cavitation. 


CONFIDENTIAL 



PREVIOUS WORK 


325 




Figure 1. Power-producing cavitation vs pulse length (Bell Telephone Laboratories). 


11. .3 PREVIOUS WORK 

A cursory searcli of the literature disclosed that 
very tittle work dealing with jtower or high-level 
operation of inagnetostrictive devices has been done. 
In the early work of Cb W. Pierce and K. C. Black, 
nearly all observations were carried out at very low 


levels of alternating excitation and limited values of 
polarizing field. K. C. Black ^ states, “. . . lor nickel 
the [electrical] reaction increa-ses to the highest 
[polarizing] field used in this experiment.” Later 
work carried out in England and in the United States 
indicates definitely that for low-level operation an 
optimum value of magnetic polarization exists. On 


(CONFIDENTIAL 






















































































































.{26 


HIGH POWER DRIVING OF MACiNETOSTRICTIVE TRANSDUCERS 


the other hand, F. D. Smith states, “In general, 
the larger the alternating field, the larger the polariz¬ 
ing field must be to obtain best working conditions.” 
Here he has a.ssumed best working conditions to 
mean greatest efficiency. He also presents evidence 
indicating that a large cross section of nickel of low 
energy density is also essential to high efficiency of 
operation. Certain modern transducer applications in 
which size and weight are important, coupled with 
the advantages of short-pulse operation, indicate 
that design for maximum acoustic output may be at 
least equal in importance to design for maximum 
efficiency. 

Smith has also emphasized the complexity of the 
problem of high-level operation. He has given data 
for annealed nickel in the form of graphs giving eddy- 
current and hysteresis losses per unit volume as a 
function of polarizing field for constant a-c amplitude 
and as a function of a-c amplitude for constant 
polarizing field. In addition, an overall core-loss 
factor is presented as a function of the .so-called eddy- 
current parametei' 


for constant a-c amplitude for various values of the 
polarizing field. Here t is lamination thickne.ss, Hr the 
reversible permeability,/frequency, and p resistivity. 
This approach and presentation of data is particu¬ 
larly adapted for delineating tran.sducer design pro¬ 
cedures but masks the practical problem of correct 
matching and tuning. Presenting the data in terms 
of the equivalent resistance and reactance of the 
device masks actual losses but assists the designer of 
the electric power source that supj)lies the transducer. 
Both methods of giving the experimental results are 
u.seful. The .'<econd method will be used here, since 
time necessitates pre.sentation of data rather than of 
quantities derived from it. 

Salisbury and Porter have described a magneto- 
strictive oscillator with a d-c power suiq)ly of 2 kw. 
With the various arrangements of oscillator coils 
which they described, a frequency range from 7,000 
to .50,000 cycles per second could be covered. From 
the dimensions of their half-wave nickel tube and the 
construction of the apparatus, the potential power 
density in the active magnetostrictive material at 
the highest frequency was 180 watts per cubic centi¬ 
meter if the fvdl 2,000 watts were used. It is doubtful, 
however, if full power was utilized at the highest 
frequency. At the lowest frequency the maximum 


potential power density was only 51 watts per cu cm. 
The transformation of electric energy into mechanical 
energy by the magnetostrictive process is only a little 
less efficient for a tube-type o.scillator than for a 
toroid. It is therefore po.ssible that Salisbury and 
Porter may have approached input power densities 
sufficient to give the idealized maximum acoustic 
output. (See Section 11.4). In view of the use of non- 
laminated nickel and the evident difficulties en¬ 
countered in cooling, it is probable that the overall 
efficiency of the equipment was low and that the 
nickel was not u.sed efficiently. No data were given 
concerning impedance measurements, efficiency, or 
estimates of the various power losses. 

11.4 IDEALIZED POWER LIMITATIONS 
OF MAGNETOSTRICTIVE MATERIAL: 

FREQUENCY DOUBLING 

In the operation of a magnetostrictive transducer 
at high power, it is important to have an estimate of 
the maximum acoustic power that the tran.sducer 
can deliver. As has already been pointed out, it ap¬ 
pears that, in the proper circumstances, it will be 
quite possible to utilize such high jjowers that the 
magnetostrictive material is the limiting factor. 
Under these conditions there will be an optimum 
wave form for the voltage or current in order that the 
limiting acoustic power be as large as possible. 

The .starting point here will be equations (9) in 
Chapter 3, viz.: 

P = —(B- + Es 

He = H — SfireBs, (1) 

where P and s are respectively the longitudinal static 
stress and strain in the magnetostrictive material, B 
and II are the total induction and field, and ip is the 
field applied by an external winding. The magneto¬ 
strictive coefficient e is one-half the slope of the 
u.sual X plotted against the polarizing induction Bo 
(.see equation (12) of Chapter 3). Now the mechanical 
portion of the system is linear. Thus, in order to de¬ 
liver large power to the mechanical system without 
generation of harmonics, the magnetostrictive stre.ss 
— eB~ should vary sinusoidally with the time at a 
frequency near resonance. Let 

B- = 4[](B-)n,ax + (^U),nin] 

+ 5[(^''‘)max — (R-)min'] CO.S 

= (R")min + C(R")m.ax “ (/U) ,„ in]) CO.s'^ — , (2) 


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IDEALIZED POWER LIMITATIONS FREQUENCY DOUBLING 


327 


where (7?-)max and (B')min are the maximum and 
minimum values of and oj is the angular frequency 
at which the motion is to take place. In order that the 
coefficient (B“),nax — (B‘)min he as large as possible, 
(^■)max should be increased to .saturation, while 
{B'),„iri goes to zero. Then 

/J- = (/^'-Iniax COS^ (3) 

The .simplest \'ariation of the induction will be 

ut 

B ~ f^max COS “ • (4) 

Thus, under the condition that no harmonics are to 
be impressed on the mechanical system, maximum 
power will be delivered at the fundamental when B 
varies at half frequency with average value zero and 
with amplitude limited by .saturation. 

The voltage across the transducer is clo.sely related 
to equation (4), since if leakage inductance and 
copper resistance are neglected, 

0)f 

E = XaB = ^AVwJ3„,ax 'Sin — , (5) 

where is the number of turns around the core, c 
is the cro.ss section and B is the time derivative of 
the magnetic induction. 

Consider a ring stack with radius a (cm), radial 
thickness b (cm), length 1 (cm). The angular fre¬ 
quency CO at resonance is E pa^ where E is the 
Young’s modulus and p the density of the core ma¬ 
terial. In accordance with the discussion above, the 
time-varying portion of the magnetostrictive stre.ss is 

E 

F = — —5^nax COS COC (6) 


Since the system is at re.sonance, its mechanical im¬ 
pedance is a pure resistance and the time derivative 
of the strain s is in pha.se with the stress. It is found 
that 


. _ 0 ^ _ 0 ^ 
'~V~pE~ E 


(7) 


where Q is the ratio of the mass and or stiffness re¬ 
actance of the ring at re.sonance to the mechanical 
resistance. From equations (6) and (7), the me¬ 
chanical power in watts per cubic centimeter of core 


Power = PslO ^ = 


E 

QcolQ- 

SE 


^“B max 

(watts/cc) . (8) 


The following numerical values for nickel are as¬ 
sumed: E — 2.1 X 10'" dynes per sq cm. 6 = —2.2 
dynes per sq cm per sq gauss, Bm^x = 6,000 gausses. 
Then, from equation (8), 

Of 

IMax power ~ — watts/cc , (9) 

5 

where / is the frecpiency in kilocycles per second. 
This is the theoretical maximum mechanical power, 
limited by magnetic saturation, that can be gener¬ 
ated j)er cubic centimeter of nickel in the form of a 



Figure 2. Calculated wave form of H and //, for nickel 
ring stack with Q = 5. 


ring. To obtain the useful radiated power, equation 
(9) must be multiplied by a “mechanical efficiency” 
that takes account of mechanical losses internal to 
the transducer. It is to be noticed that equations (8) 
and (9) are proportional to the fourth power of the 
maximum induction. Thus, for example, if the value 
a.ssumed is reduced from 6,000 to 5,000 gaus.ses, the 
maximum power is approximately halved. 

Equation (9) was derived for a ring stack. Similar 


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HIGH POWER DRIVING OF imagnf;tostric:tive transducers 


.12« 



UNDER TEST HYDROPHONE 

Figure 3. Schematic diagram of experimental setup. (Note: Ground point of bridge should he lettered JS; opposite 
junction, A.) 


formulas giving lower maximum power hold for other 
forms. Thus equation (8) holds for a half-wave rod 
if an additional factor 8 V- is inserted on the right. 
In general, the multiplying factor is the ratio of the 
squared average stress throughout the core to the 
at'erage squared stress. 

The wave form of the voltage has already been 
given l)y equation (5). Being sinusoidal, it can be 
attained by operating the transducer from a gener¬ 
ator with low impedance and good wave form. The 
wave form of the current that is proportional to He 
will then depart appreciably from sinusoidal. Cal¬ 
culated wave forms for H and He for a nickel ring 
stack, the Q of which is 5, are shown in Figure 2 
for 5nua.x = 5,000, 5,500, and 6,000. 

The presence of harmonics in the current wave 
form suggests the possibility of applying a small per¬ 
centage of harmonics to the exciting voltage. In the 
case of the triode vacuum-tube oscillator operating 
at high levels, it has been shown that the introduc¬ 
tion of a small per cent of harmonic voltage in the 
system properly phased with respect to the funda¬ 
mental increases the efficiency of the oscillator. 
Possibly a similar result would apply to a magneto- 
strict ive device. 


11.. 5 EXPERIMENTAL STUDY AND 

DESCRIPTION OF RESULTS 

11 .. 3.1 Method and Equipment 

It would be desirable to approach the problem of 
high-level operation experimentally from the point 
of view of steady-state measurements, so that con¬ 
ventional methods might be used. However, if the 
object is to ascertain a useful upper limit of electric 
power to be delivered to the magnetostrictive ma¬ 
terial, heat is certain to be a limiting factor. As 
already pointed out, the theoretical upper limit of 
acoustic output power per unit volume of active mag¬ 
netostrictive material leads, even on the basis of the 
most optimistic efficiencies, fo values of electric input 
powers far greater than can be di.ssipated without 
elaborate cooling means. Hence some form of inter¬ 
mittent operation must be used. This leads to 
difficidties in determining the electric input powers. 
Under the circumstances, the use of a pulsed-power 
bridge seemed most feasible. This permits of direct 
measurement of effective resistance and reactance. 
With measurement of the voltage across the tran.s- 
ducer, electric input powers can be determined from 
the resistive component. Effective values of the 


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EXPERIMENTAL STUDY AND DESCRIPTION OF RESULTS 


329 


permeability may be computetl from the reactive 
component. 

Fig:ure 3 shows schematically the experimental ar¬ 
rangement which was used. Pul.ses of approximately 
10 -milliseconds duration were applied roughly twice 
a second to the suppre.‘Jsor grid of a switching tube on 
the control grid of which a steady voltage of the 
desired ultrasonic frequency was continuously im¬ 
pressed by the Western Electric 17B oscillator. Thus 
trains of several hundred cycles length were jjeriod- 
ically impressed through an efficient impedance- 
matching transformer across the terminals of a 
resonance bridge. Balance was attained l)y proper 
adjustment of K and C, using a cathode-ray oscillo¬ 
scope with synchronized sweep as the bridge detector. 
.\ step attenuator controlled the input of the power 
amplifier so that a wide range of voltage could be 
ai^plied to the bridge. Measurements of effective re¬ 
sistance and reactance as a function of the alternating 
excitation level could then be made. This pulsed- 
bridge technique allowed investigation of fairly high 
levels of transducer excitation using ordinary stand¬ 
ard measuring equipment without overheating any 
of the components. 

During the course of the measurements, one di.s- 
advantage of the resonance bridge method was en¬ 
countered. If the reactance of the transducer becomes 
capacitative during a run, either an appropriate 
capacitor must be added on the other side of the 
bridge, or a variable inductor must be introduced in 
series with the transducer under test. Either of the.se 
solutions is undesirable. In the first case the trans¬ 
ducer will be untuned and the resultant power factor 
may reduce the level below that desired though, 
if a generous supply is being used, this may not be a 
■serious handicap. In the second case the inductor 
introduces a troublesome resistance correction factor 
and the necessary means of f)locking the d-c polariz¬ 
ing current from parallel paths is lost. In many cases, 
however, the resonance bridge is adequate and little 
inconvenience is experienced. 

In order to correlate ob.served measurements with 
theory, a number of precautions must be observed. 
Ideally the wave form of the voltage across the 
tran.siducer must be sinu.soidal and uninfluenced by 
the .source. A zero-resistance generator would be 
ideal. To achieve this effectively is difficult. Strictly, 
all bridge measurements would be ruled out under 
.such conditions, since one arm of the bridge in series 
with the unknown would always vitiate the.se ideal 
assumptions. Factors influencing wave form can. 


however, be minimized. An obvious precaution is to 
reduce the internal impedance of the .source to as 
low a value as possible. This is done most simply by 
employing voltage feedback in a conventional man¬ 
ner. The amplifier emi)loyed in this work was 
originally designed for steady-state continuous meas¬ 
urements and voltage was fed back from a special 
winding on the output tran.sformer to the cathodes 
of the e.xciting stage. A complete diagram of this 
unit, including power .supplies, is shown in Figures 4, 
5, and 6. The power sujjplies consist of four units. 


CANNON 



Figure 4. High-voltage supply. 


A 2,000-volt unregulated unit (Figure 4) was pro¬ 
vided for the plate supply of the final power ampli¬ 
fier pentode stage (Type 828 tubes). A stabilized 
screen supply (Figure 5) was provided for the 828 
tubes. This unit, taking part of the control grid 
voltage for its amplifier stage from the input side of 
the series regulator tube, could be adjusted to have 
perfect voltage stabilization and e.ssentially zero in¬ 
ternal resistance for a given load. A bias supply and 
another stabilized supply for general utility purposes 
completed the four units. This arrangement provided 
flexibility of control for the experimental work that 
was carried out. Stabilization of the .screen voltage 
assisted materially in maintaining constant ampli¬ 
tude wave train in any one pulse. The internal re- 


CONFIDENTIAL 










































330 


HIGH POWER I)RIVIN(; OF jMAGNETOSTRICTIVE TRANSDUCERS 



Figure 5. Stabilized screen supjily. 


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EXPERIMENTAL STUDY AND DESCRIPTION OF RESULTS 


331 



sistance of the power amplifier was found liy varying 
the value of a resistive load and plotting the resist¬ 
ance R against the reciprocal of the load current. A 
typical example of the data resulting is shown in 
Figure 7. The intercept on the negative R axis gives 
the internal resistance. It can he .seen that the in¬ 
ternal resistance is approximately one-third the value 
of the design output resistance. This value might be 
reduced by proper adjustment of the voltage feed¬ 
back. In future equipment, means .should l)e provided 
for altering the feedback and thus determining the 
effect of this internal re.sistance in any particular 
ca.se. Purity of wave form requires operation of the 
power amplifier well below its overload point. It is 
desirable to have exce.ss power available. 

The amount of power needed for an investigation 
of this sort can be estimated roughly from the 
theoretical upper limit of acoustic output. This is of 
the order of Qf 5 watts per cubic centimeter of 
actively working nickel for a toroid, as discu.s.sed 
earlier in the chapter, where / is in kilocycles and Q 
is the so-called Q in water. If a rea.sonable overall 
efficiency of 30 per cent is a.s.sumed, and if / may be 


suj^po.sed to vary between 10 and 00 kc while Q lies 
between 1 and 10, then rea.sonable iqiper limits of 
electric input power per cubic centimeter of actively 
working nickel would range between 6.6 and 600 
watts. The possible magnitude of the cooling problem 
if steady-state measurements were attempted is evi¬ 
dent. Table 1 lists the active volume of nickel in 
several practical tran.sducers and the upper limit of 
power which it would be desirable to have availal>le 
(even with no margin for con.servative operation) if 
high-level studies are to be made within the assump¬ 
tions mentioned above. 

The resistive components of the bridge must be 
able to dissipate the average power put into the 
transducer. For the pul.se length and repetition 
frequency quoted, the average power is of the 
pulse power. More difficulty will probably be en¬ 
countered at lower levels with the decade resistance 
than with the decade conden.ser. In the equipment 
under de.scription a standard General Radio com- 
pen.sated decade resistor Type 670-F was used. The 
manufacturer states that 34 watt per unit of resist¬ 
ance in each decade is allowable if the limit of tem- 


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HIGH POWER DRIVING OF MAGNETOSTRIGTIVE TRANSDUCERS 


:{;$2 


perature rise is to be 40 C. Within this limit the 
resistance change is less than 0.1 per cent. For a 
decade of tenths, unit, and tens, allowable currents 
are 11.3, 3.5, and 1.1 amp, respectively. The lack of 
other compen.sated decade resistor ranges limits the 
impedance range of transducers that can be measured 
in a resonance bridge employing 1 1 ratio arms. 

The decade tuning condenser employed in the 
bridge was specially constructed of GR Type 505 mica 
condensers, each unit of which, con.servatively, will 
di.ssipate 1 watt. Peak voltages of 500 \'olts are per¬ 
missible acro.ss any of the conden.ser units. With a 
dissipation factor of less than 0.1 jier cent at all 



Figure 7. Determination of internal resistance of the 
power amplifier. 


frequencies between 10 and 90 kc, it is not believed 
that any serious limitations wilt be imposed by the 
mica condenser as used in .such a pulsed-bridge appli¬ 
cation. However, care should be taken with the con¬ 
tacts involved in the switching of the various units 
in a decade. 

The bridge shown in Figure 3 was used with a I T 
ratio to minimize errors in making all measurements. 
One terminal of the transducer was ordinarily effec¬ 
tively grounded at one of the detector junctions of 
the bridge. A cathode-ray oscilloscope with .syn- 
chronized sweep was u.sed to measure the voltage 
across the transducer and to observe its wave form. 


Current wave form was observed by inserting a 
small 3^-ohm resistor lietween the transducer T and 
the grounded junction of the bridge, amplifying the 
voltage across it, and by ob.serving the resultant 
pattern on a synchronized cathode-ray oscilloscope. 
These o.scilloscopes were calibrated by steady-state 


T.\bee 1 


T raiisducer 
type 

Xoiniiial 

res. 

freq. Q 

kc 

•Active volume of 
magnetostrictive 
material jier cm 
.stack height 

Power 
required per 
cm of 

stack height 

SPEP element 

.58 

8 

0.60 cm^ 

192 watts 

HP-3 

24 

9 

2.33 cnP 

336 watts 

Thick-walled 
60-kc ring 
stack 

60 

10 

3.49 cm3 

1,390 watts 

Thin-walled 
ring stack 

60 

5 

1.93 cnP 

386 watts 


Computed on basis of Bmax = 6,000. fSee numerical v'alues used in 
equation (8)]. 


voltages of the same frequency as used in the bridge 
measurements. A GR shielded transformer was used 
for isolating the chain of equipment between the 
detector junctions of the bridge T and B and the 
final cathode-ray oscilloscope detector. For sufficient 
sensitivity, considerable amplification was neces.sary 
in the detecting circuit. As balance at the funda¬ 
mental frequency was approached, amplification was 
increased, ffarmonic voltages then predominated and 
tended to mask the balance. It was found ab.solutely 
necessary to insert a high-discrimination low-pass 
filter between the bridge and the o.scillo.scope indi¬ 
cator. Three filters were built with the cutoff fre¬ 
quencies so disposed that it was always possible by 
proper filter selection to obtain high discrunination 
against harmonics of the mea.suring frequency. Cut¬ 
off frequencies were placed at 33, 67, and 100 kc. 
Each filter consisted of three /n-derived .sections, 
having m equal 0.7, 1, and 0.8, terminated in two 
//(-derived half sections, /// = 0.6. Each section or 
half section was j/laced in a separately shielded com¬ 
partment, and for the 33-kc cutoff unit a full 80-db 
discrimination was realized. For the other two units 
the discrimination was slightly le.ss. This amount of 
di.scrimination was needed and more would have 
been useful under .some conditions of operation. The 
filters were designed to operate between 600-ohm 
terminating resistances. Complete design data are 


CONFIDENTIAL 








































































EXPERIMENTAL STUDY AND DESCRIPTION OF RESULTS 




given in Table 2. To insure proper termination under 
various bridge adjustments, a cathode follower ad¬ 
justed to have the proper output resistance was used 
between the bridge isolating transformer and the 
filter input. 

A B-19H hydrophone, described in ('hai)ter 6, was 
used as the detector of sound emitted from the tran.s- 


«0 

*0 

20 



^0 

HHi 


jHHj 


U009 ‘o 

Hh 






(jm. 


HH 

- 

StSlSL 


T.cble 2. Frequencies in kc, inductances in inh, capac¬ 
ities in yuf. 


Filters 

I 

II 

III 

Cutoff freq. = 

h 

33 

07 

100 

Freq. of 
infinite 

m = .6 

41.2 

83.7 

125 

attenuation 

m = .7 

4fi.2 

93.8 

140 

= /=o 

m = .8 

5.5.0 

111.8 

107 


U 

1.730 

0.8553 

0.5727 

Values of 

L> 

4.051 

1.990 

1.330 

inductance 

U 

5.787 

2.851 

1.909 


La 

4.030 

2.281 

1.527 


c, 

0.00857 

0.004223 

0.002829 


C-, 

0.01045 

0.005147 

0.003449 

Values 

c. 

0.002929 

0.001442 

0.000900 

of 

Ca 

0.01307 

0.000730 

0.004510 

capacitance 


0.01447 

0.007120 

0.004775 


c. 

0.001809 

0.000891 

0.000597 


c. 

0.01125 

0.005.542 

0.003714 


ducer under test. Its respon.se was amplified and 
calipers used to measure the amplitude of the syn¬ 
chronized pid.se pattern on a calibrated cathode-ray 
o.scilloscope. 

Measurements were made on the following lami¬ 
nated stack elements. 

1. SPEP stack, as described in Chapter 7. 

2. Thin-walled 2V-Permendur ring stack. 

3. Specially annealed ring stacks [SPARS] of 
nickel of various thicknesses. 

11 .. 5.2 jVIeasuremeiits on SPEP 

Elements 

A single SPEP element with permanent-magnet 
polarization, described in considerable detail in 
Chapter 7, was first investigated. This element was 



Figure 8. Pressure cliainher. 

mounted inside a chamlier lined with butyl rubber to 
minimize reflections and filled with degassed castor 
oil under pressure to avoid cavitation difficulties. A 
flexible metal tubing led from this to the compression 
chamber of a .small hydraulic automobile jack. One 
end of the chamber was enclosed by pc ruliber with 
a supporting cover of He-hi. stainle.ss-steel expanded 
metal with diamond-shaped mesh openings approxi¬ 
mately 1^ X % in. in .size. A small direct-reading 
pressure gauge was attached and pre.ssures up to 5 
atm were ordinaril 3 ^ used during power testing. Fig¬ 
ure 8 shows A, a front view of the pre.ssure chamber; 
B, a specially constructed transducer element 
mounted on the backplate of the pre.ssure chamber; 
and C, the modified j)ipe-saddle mounting arrange¬ 
ment used for holding the chamber in the .sound ab¬ 
sorbent tank. Figure 9 shows the a.s.sembled pressure 
chamber, hydrostatic pre.ss, and B-19H hydrophone 
mounted for u.se in the ab.sorbent tank. Two different 
means of mounting the SPEP stack in the chamber 
were utilized. The first is shown schematically in 
Figure 10. 


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33t 


HIGH POWER DRIVING OF IMAGNETOSTRIGTIVE TRANSDUCERS 



Figure 9. Pressure chamber iu tank. 



Figure 10. Original SPFiP mounting in castor oil. 


The STEP stack was immersed directly in castor 
oil. A slight lowering of the Q of the device was ob¬ 
served and was thought to be caused by additional 
damping added by the oil. A different mounting was 
then arranged, as shown in Figure 11. Here the stack 
was Cycle-Welded to a truncated conical rubber dia¬ 
phragm, which in turn was Cycle-Welded to a steel 
supporting plate. This supporting plate closed one 
end of a steel housing so that air and sponge rubber 
rather than oil now surrounded the stack itself. This 



Figure 11. Mounting of element with rubber face. 

closely simulated the mechanical arrangement of one 
element of a full 32-element SPEP transducer. 

This type of mounting, in which the rubber dia¬ 
phragm was an appreciable fraction of a wave length 
in thickness, gave rise to the air vector impedance 
locus shown in Figure 12A. However, when the same 
characteristic was mea.sured in water, the locus 
changed to that shown at B. For both A and B, plots 
of R and A" again.st frequency were made and the 
purely motional components were separated out as 
previously described in Chapter 2. A plot was then 
made of the square of the motional impedance against 
frequency, as shown in Figure 12C for both the air 
and water cases. Since the motional impedance is 
nearly proportional to the amplitude of vibration, 
this plot shows roughly the frequency distribution of 
mechanical energy. It is interesting to point out that 
this system, ha\dng more than one simple mode of 
vibration, exhibits characteristics typical of two 
coupled electric circuits when the coupling is altered 
by changing the loading. 

Figures 13 and 14 show typical curves of resistance 


CONFIDENTIAL 







































IN OHMS 


EXPERIMENTAL STUDY AND DESCRIPTION OF RESULTS 


335 




R IN OHMS 

VECTOR IMPEDANCE LOCI 


R IN OHMS 



FREQUENCY IN KC 


Figure 12. Impedance curves of element mounted as in Figure 11. .A. In air. R. In water. C. Energy distribution 
in air and in water. 


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HIGH POWER DRIVINC; OF MAGNETOSTRICTIVE TRANSDUCERS 


:{:{6 













0.3 AMPS 









ae AMPS 






1.2 AMPS 









1.8 AMPS 











'•V 

V 


?j4AMPS 









3.0 AMPS 

































-JOINS P 

OINTS A 

r WHICH 

PEAK A C * POL 

ARIZING C 

URRENT 


o'--------- 

,05 0.1 0.2 0.3 as 0.7 I 2 3 5 

AC IN AMPERES 

Figure 14. Reactance of element as a function of level and polarizing current. 


and reactance of a SPEP unit with d-c polarization 
as a function of excitation level for various values of 
polarizing current. In general it should be noted that 
both resistance and reactance increa.se much more 
rapidly when the peak value of the alternating field 
exceeds the fixed polarizing field. All these measure¬ 


ments were made at or near the resonant frequency. 
Figure 15 presents the same data in a different way. 
It shows sections of the curves of Figure 13, illus¬ 
trating the changes that occur at constant a-c level 
when the polarizing current is ^'aried. 

The first high-level driving experiments were made 


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EXPERIMENTAL STUDY AND DESCRIPTION OE RE;SULTS 


337 



Figure 15. Resistance of constant-current driving as a 
function of polarizing current. 


resistive eonipouent of the device was not deter¬ 
mined. Impedance data at low signal levels were 
taken so that a rough estimate of the resistance could 
be determined by interpolation from the data of 
Figure 13. Input jiowers were computed and aver¬ 
aged values of data derived from sev'eral runs are 
shown in hdgure 16. The data are shown only becau.se 
higher levels were reached in these particular runs 
than later, when the available power was divided by 
the bridge. It is to be noted that although a linear 
relationship exists between input and output for in¬ 
put power as great as 30 watts, the slope of the line 
deviates considerably from unity. It is quite prob- 
alile that the values of resistance used are in error 
as experimental evidence was found .showing con¬ 
siderable variation in flux density in the legs of the 
PM unit. Later data taken using the bridge tech¬ 
nique and a d-c polarized SPEP unit gave plots in 
which the .slope was nearly unitj^ over a wider range. 
A typical curve is shown in Figure 17A. The.se later 
data, though considerably more reliable, are much 
more limited in range. 

Data such as Figure 17A .shows were used in cal¬ 
culating the total acoustic output to be expected from 
one of the 32-element SPEP transducers. The ele¬ 
ments of this unit were not all wound with the same 
number of turns. There were four 50-turn, eight 31- 



on a permanent magnet [PM] SPEP stack before the turn, four 20-turn, eight 15-turn, and eight 9-turn 
pulsed-bridge technicpie had been adopted. The cur- elements arranged to produce the desired pattern of 
rent through the transducer was measured but the acoustic output. In order to estimate the power 


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HIGH POWER DRIVING OF MAGNETOSTRICTIVE TRANSDUCERS 





WATTS INPUT 


Figure 17. Output vs input of a d-c polarized SPEP. 


handling capabilities of this unit, it is necessary to 
find the number of normal oO-turn elements to which 
the complete shaded unit is equivalent. By assuming 
that the power absorlied in ant" element is ju'opor- 
tional to the square of the number of turns in the 
windings, it is found that 8.7 50-turn elements would 
be eciuivalent to the 32-element shaded units in 
power-handling capacity. This factor is u.sed to multi¬ 
ply all powers measured on a single element. Figure 
18 shows the acoustic output of the 32-element unit 
predicted from the data of Figure 17A and the 
shading factor 8.7, assuming an efficiency of 30 per 
cent. This extrapolation from the .single element to 
tlie complete 32-element shaded unit involves a num¬ 
ber of assumptions, and the result given agrees only 


roughly with the best experimental work that has 
been done on the 32-element. as.sembled unit. In 
order to test the effect on the pattern of a high level 
of operation, input jiowers as high as 1,300 watts 
were used and at this level the measured acoustic out¬ 
put was 400 watts. This is to be compared with the 
value of 275 as read from the curve of Figure 18. 
The patterns at the 1,300-watt and 150-watt levels 
were e.ssentially the same. 

Since the theory worked out under Section 11.4 
implies operation with no polarization, it was of in¬ 
terest to compare the acoustic outputs of the polar¬ 
ized and nonpolarized ca.ses. Nonpolarized operation 
offers attractive possibilities for certain applications, 
since it involves applying a driving voltage of half 


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EXI'EKIiVIENTAL STUDY AND DESCRIPTION OF RESULTS 


:i;i9 


3V3 CYCLES 



Figure 18. Output vs input of 32-element SPEP transducer. 


the frequency of mechanical re.sonance. This lowering 
of the frequency increases the range within which it 
might be possible to emjtloy highly efficient gas tube 
oscillators. In Figure 17B is shown a plot of acoustic 
output vs electric input for half-frequency driving. It 
is interesting to note that for the half-frequency use 
the efficiency is increasing continuoasly with level. 
The dotted extrapolation suggests the possibility that 
at very high input levels nonpolarized operation 
might equal or exceed the efficiency of that with 
polarization. Regardless of efficiency, nonpolarized 
operation might in some cases be definitely advan¬ 
tageous. F'igure 19 shows the typical change of R and 
A' with level for the nonpolarzied case. These data 
were taken on the same d-c SPEP unit lused in the 


half-frequency driving tests. Comparison with Fig¬ 
ures 13 and 14 shows the e.ssential difference in char¬ 
acter of these changes with level. A maximum in the 
re.sistance curve at fairly low v’alues of peak // is the 
most distinguishing feature. This will be referred to 
later in connection with the work on laminated ring 
stacks, where there is greater possibility of correlating 
the results with theory. 

It is of interest to investigate what changes take 
place in the impedance curves as a function of power 
level. Since this is unimportant for receiving hydro¬ 
phones where the power levels are usually very low, 
the jiractice of making impedance measurements at 
.some low but unspecified level became established at 
IIUSL. At power levels usually encountered in pro- 


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HIGH POWEK DRIVING OF MAGNETOSTKIGTIVK TRANSDUCERS 





Figure 19. Resi.stance and reactance of a nonpolarized 
SPEP as a function of driving current. 



RESISTANCE-ohms 


Figure 20. Variation of impedance loci with driving 
current. 

jector operation, the changes in K and with level 
cannot be neglected. 

A series of runs was made on a single SPEP ele¬ 
ment in the pressure chamber, keeping the frequency 
in each run constant and varying power level. Plots 
of R and A' against driving current were then made. 
For each of several constant values of current, R 
and X were determined by sectioning the above- 



RESISTANCE IN OHMS 

FiGtmE 21. Variation in impedance loci with input 
power. 



Figure 22. Observed changes in impedance loci due to 
heating and subsequent cooling. 


mentioned curt'es and the residting vector imped¬ 
ance loci plotted as in Figure 20. Similarly, the 
original t'alues of R and X were plotted against power 


C()XFIDFNTL\L 









































































































































































































EXPERIMENTAL STUDY AND DESCRIPTION OE RESULTS 


341 



Figure 23. Re.sistance of 2V-Permpn(Iur ring stack a.s a 
function of driving level. 


and the resulting vector impedance loci for various 
values of constant power are plotted in Figure 21. 
Because of the difficulty of computing the core im¬ 
pedance for the geometry of the .SPEP element, no 
attempt was made to derive the strictly motional 
impedance diagram. The change with level from a 
fairly circular locus to an elongated egg-shaped one 
is common to both Figures 20 and 21. It is l)elie\ ed 
the power level was sufficiently high to extend well 
into the region of magnetic nonlinearity. At this 
point it is not known what significance can be at¬ 
tached to the.se families of curves. They are shown 
primarily to indicate typical changes in the loci that 
occur as a result of changes in driving level. 

Figure 22 exhibits another type of change that may 
take place in the vector impedance loci of units polar¬ 
ized by sintered-oxide magnets if the unit is sub¬ 
jected to an appreciable temperature change. Here 
the SPEP element was heated by the application of 
alternating current of resonant frequency. Its tem¬ 
perature was determined by a thermocouple placed 
between the two windings and just below the arch of 



Figure 24. Reactance of 2V-Pci'mcn(lur ring stack as a 
function of driving level. 


the core. After reaching the temperature indicated, 
the unit was allowed to cool to room temperature. 
Low-level impedance measurements were then made. 
The permanent changes in imjtedance are typical of 
a decreased polarization and are probably com¬ 
pletely accounted for on this basis. This particular 
experiment does not of itself provide sufficient evi¬ 
dence to decide the role played by each of several 
possible factors. The decrea.se in strength of the 
sintered-oxide magnet may be ascribed to the effect 
of temperature, to prolonged application of a strong 
a-c, to a single pulse of high intensity, or to a combi¬ 
nation of two or more of these causes. A great amount 


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312 


HIGH POWER drivim; ok ma(;netostri(:tive transducers 



Figure 2r>. Impedance curves of 2V-Permendur for 
v'arious constant values of driving current. 


of experimental euidence exists to indicate that high- 
level pulsing, with low average power and hence very 
little production of heat, jtroduces no permanent 
changes in impedance in units polarized by perma¬ 
nent magnets. 

11..5.3 Measurements on the 2\ - 

Permendnr Stack 

Figures 23 and 24 show the resistance and react¬ 
ance change as a function of level for a thin-walled 
2\'-Permendur ring stack. Here the total percentage 
change in R and X is con.siderably greater than for 
the SPEP element of annealed nickel. Figure 25 
shows a family of vector impedance loci plotted from 
data obtained by sectioning the cur^■es of Figures 23 
and 24 for various constant values of current. The Q 
of the device is so low that the vector impedance locus 
does not even open at resonance and at this frequency 
only an indentation ajipears in the curve. As the level 
increases, this bunq) becomes less ])ronounced until 


MEAN DIAMETER : 1.06 INCHES 
RADIAL WALL THICKNESS = .090INCHES 



Figure 2(1. Drawing of SP.\RS lamination with 
dimensions. 

at a level of 1 amp the locus has become e.ssentially a 
smooth curve giving no indication of resonance. 

11 ..3 .1 Measurements on Annealed- 
Niekel Ring Staeks 

A series of thin-walled SPARS (Figure 26) were 
constructed with the expectation that the data from 
this geometrically simple transducer would be help¬ 
ful in formulating a theory of high-level lo.s.ses. The 
nominal resonant frecpiency was 60 kc. Lamination 
thicknes.ses of 1, 3, 5, 10, and 25 mils were cho.sen. 
.All laminations were given the same heat treatment, 
but apparently differences in magnetic properties 
arise during the rolling process which are not re¬ 
moved by subsequent heat treatment. Tests made by 
the routine methods described in Chapter 4 .showed 
considerable variation in magnetization curves, per¬ 
meability, and hysteresis loops among the different 
samples. Magnetization curves are shown in Figure 
27 and major hysteresis loops in Figure 28. 

In order to study effectively the operation of a 
magnetostrictive transducer under high-level oj^er- 
ation, it is first necessary to understand core effects 
at high level without the complication of the mag¬ 
netostriction. Con.sequently, the laminated stacks 
were first wound tightly with 70 turns of wire over a 
thin insulating layer of silk tape and measurements 


CONFIDENTLAL 




























































FAPERLMENTAL STUDY AND DESCRIPTION OF RESULTS 


3t:{ 



were made to determine the low-level value of react¬ 
ance and a-c resistance. In order to obtain the true 
value of the inductance, it was necessary to carry out 
the measurements at such a low frequency that the 
effect of eddy currents would be negligible. Experi¬ 
mentally this is determined when the curve of meas¬ 
ured inductance plotted against frequency ap¬ 
proaches a constant as frefiuency is reduced. In terms 
of the eddy-current theory developed in Chapter 3 
this means that the ratio///c is much le.ss than unity. 
The stack of laminations of 0.025-in. thickness 
showed variations in inductance at frequencies well 
below 1,000 cycles, so that it was necessary to extend 
the measurements to frequencies as low as the avail¬ 
able apparatus would permit. To judge from the 
value of fc computed for the 25-mil lamination and 
the slope of the experimental inductance curve, it is 
doubtful if measurements were carried to as low a 
frecpiency as was desirable. iNIeasurements of re¬ 
sistance vere originally made between 10 and 90 kc. 
In this frecpiency range the core of thickest lamina¬ 
tion proved to have less resistance than some of the 
thinner .samples. This rather unexpected result 
stimulated the taking of data over as wide a fre¬ 
quency range as easily available equipment per¬ 
mitted. Figures 29 and 30 .show families of R and L 


respectively as a function of frequency for the 
samples of different thickness. 

In making measurements over the frequency range 
shown, it was necessary to use three different bridges. 
Below 2,000 cycles a Heaviside bridge using a Camp¬ 
bell mutual inductometer was used. By reversing the 
1/1 ratio arms and by u.'^ing a substitution method, it 
was possible to measure consistently resistances of 
less than 0.1 ohm. At these low frequencies it was 
impo.ssible to u.se an o.scilloscope detector without 
high-discrimination low-pa.ss filters to eliminate har¬ 
monics; a GR wave analyzer was finally used for this 
purpo.'^e. Between 2,0(K) and 10,000 cycles a direct- 
compari.son four-arm inductance bridge was used. 
Above 10 kc the standard re.sonance impedance 
bridge described in Chapter 9 proved entirely ade- 
cpiate. During the course of the.se measurements, 
variations in R and L were observed at very low 
levels. Figure 31 shows an e.xample of this, again 
emphasizing the importance of specifying power 
level when electrical measurements are made on coils 
having ferromagnetic cores. 

In Figure 29 the distinct cro.ssing-over of the 
curves of resistance vs freciuency on going from the 
thick to thin laminations can be easily explained 
in terms of the classical theory of eddy currents in 


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hi(;h powkk dkim.ng of magnetostrictivi: transducers 





0 


10 

H IN OERSTEDS 


20 



Figure 28. Hysteresis loops of SPARS stacks. 


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KXI’ERIMENTAL STUDY AND DESUKIFTION OF RESULTS 


345 



Figure 29. Resistance of SP.\RS stacks as a function 
of frequency at low levels. 


flat laminae. The core impedance for the toroidal¬ 
shaped cores used in these experiments is given in 
equation (6) of Chapter 3 as 

7.C = jwLoX = — jxi) = wLnXi + jo^LoXn- 

Figure 1 of Chapter 3 shows that Xi passes through a 
maximum at approximately///c = 2.5, that for small 
values of the variable f/fc it approaches the limiting 
value if/fc, ^tnd that for high values the limit be¬ 
comes V/c/2/. For two geometrically similar samples 
differing widely in values of fc, there will be a fre- 
cpiency somewhere between the two values of fc at 
which they will have the same value of xu If should 
thus be possible to predict the crossov'er frequency 
with an accuracy dependent on the degree to which 
the assumptions are satisfied, namely fd » /» /r2- 

At the crossover point, 

Ri = wLo.x., (for tire sample with high/c) 

/C = wLo,x .2 (for the sample with low/J. 

It is assumed that the total resistance arises only 
from the effect of eddy currents, copper and hys¬ 
teresis losses being neglected. 

In all cases then, 

-CoiXl'l Co2Xi2 


and if /r, » / » then 



For the toroids under discussion, Lq, and 7>o, differed 
only because of slightly different cross-sectional (Ai 
and At) areas and different permeabilities. By taking 
this into account. 



which with rearrangement yields the expression 



The following are the values of the constants 
necessary to apply the above equation to the data 
of Figure 29. 

Lamination 


thickness 

0.001 

0.003 

0.005 

0.010 

0.025 

(in inches) 

Mo from mea¬ 
sured Lo 

87 

86 

115 

124 

226 

(Figure 31) 

.4, cross-sec¬ 
tional area 

0.151 

0.138 

0.149 

0.139 

0.146 


in sq cm 
fc in cycles 

per sec. 7.2x10^ 8.06x10' 2.18x10' 5.06x10'' 4.45x10-’ 

using 

tabulated mo 

Here/c was calculated from equation (2) of Chap¬ 
ter 3. By using the above values, the frequencies 
were calculated at which the curve for the 25-mil 
lamination crosses successively the curves for the 
10-, 5-, 3-, and 1-mil samples. The values are as 
follows. 

Calcu- Ob- Fvxamination of Assumption 
Crossover lated served fci 'A> fn 

0.02.5-0.010 5.7x10" 7.0x10" 5.06x10" 5.7xlO"»4.45xlO" 

0.025-0.005 1.5x10' 2.1x10' 2.1x10' 2.Ixl0'»4.45x10" 

0.025-0.003 4.6x10' 4.6x10' 8.06x10' »4.6xl0'»4.45xl0" 
0.02.5-0.001 1.9x10" 1.8x10" 7.2x10" » 1.8xl0"»4.45xl0" 

The last column shows that only in the last two 
cases could even a qualitativ'e agreement be ex¬ 
pected between the calculated and observed values. 

Exploratory measurements of resistance and re¬ 
actance as functions of the applied field were carried 
out for three of the five samples, namely the 1-, 5-, 
and 25-mil cases. Because of lack of time it ap¬ 
peared that this .selection would give the best survey 
of representative phenomena, since it included the 


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346 


hk;h power driving of ma(;neto.strictive transducers 



P'lGURE 30. Itiductance of SP.\RS stacks as a function of frequency at low levels. 




Figure 31. Variation in resistance and inductance for very small applied fields. 


two extremes of lamination thickness as well as that 
of which most of IIUSL’s practical transducers were 
constructed. 

Figures 32, 33, and 34 present most of this ob¬ 
servational data in appioximately 90 curves. In all 
cases the.se figures show plots of resistance and re¬ 
actance as a function of the peak applied alter¬ 
nating field H, measured by the pulsed-bridge 
technicpie. As noted earlier, the changes in re.sistance 


and reactance appeared to differ in character, de¬ 
pending on w hether the samjile under test was or was 
not subjected to a steady d-c polarizing field. Ac¬ 
cordingly, three types of data are jiresented, namely 
nonpolarized (Figure 32), polarized (Figure 34), and 
what has here been called transition data (Figure 33). 
This latter shows the gradual shift from the non¬ 
polarized to jjolarized type when measurements are 
made for succes.sively increasing values of steady 


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EXPERIMENTAL STUDY AND DESCRIPTION OF RESULTS 


:U7 





Figure 32. Resistance and reactance of unpolarized SP.VRS as a function of peak alternating field at different fre¬ 
quencies. 


jiolarization //q. The range of //o extends from values 
that are small compared with the peak alternating 
field H for most of a test to values large enough to 
exhibit the characteristics of a typical polarized case. 

Figure 32 shows the nonpolarized case, with fre- 
tpiency the parameter in each family of curves. The 
range of this parameter was determined roughly by 
the required magnitude of the bridge components 
and their believed frequency characteristics. Fre¬ 


quencies in the neighborhood of the mechanical 
resonance of the stacks were avoided in order to 
minimize motional magnetostrictive effects. Values 
of 20, 35, 50, 70, and 85 kc were chosen. The out¬ 
standing characteristic of these families is that there 
is a maximum in the majority of the curves for rela¬ 
tively low values of H. In a rough way this maxi¬ 
mum may be accounted for in terms of the vari¬ 
ation of permeability with peak driving field H. 


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HIGH POWER DRIVING OF MAGNETOSTRICTIVE TRANSDUCERS 


:U8 







Figure 33. Re.sistaiice and reactance of SP.\US as a function of peak alternating field for different values of polarizing field. 


Figure 35 shows a plot of = B H for the O.OUl-in. 
lamination. This curve has a maximum at 6 oersteds. 
It was then assumed that // varied sinu.soidally with 
time, and for each of several peak values of // aver¬ 
age values of permeability J1 were computed. These 
are shown plotted on the same area as a function of 
//. The net result is to lower the effective perme- 

^ A * 

ability for any given H below a])proximately 9.S 
oersteds and to increase it for H above that value. 


At the same time the maximum is shifted to about 
8.5 oersteds. The curve of reactance for 20 kc in 
Figure 32B has its maximum at slightly over 8 
oersteds. 

On the other hand, the variational permeability 
measured near a steady Bo = 3,800 gausses increases 
smoothly as the variational amplitude is increased.' 
This accounts in general for the two main types of 
data obser\-ed. For both the 1-mil and 25-mil cases 


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EXPERIMENTAL STUDY AND DESCRIPTION OF RESULTS 


:m9 






Figure 34. Resi.stance and reactance of polarized SPARS 
and constant value of polarizing field. 


the maximum is without exception common to all 
resistance and reactance curves. Similarly, in all 
cases the maximum in the resistance appears at 
lower values of H than the maximum m the cor¬ 
responding reactance curves. For both resistance and 
reactance this maximum moves toward higher values 

A 

of H as frequency increases. 

The families for the 5-mil stack exhibit char¬ 
acteristics .slightly different from those common to 



..s a function of peak alternating field at different frequencie.s 

both a thinner and a thicker lamination. Here the 
maximum in the resistance curve is less pronounced. 
At the lowest frequency it occurs at a value of H 
equal to or higher than that at even the highest 
frequency in the other two cases. The shift of this 
maximum toward higher H is more pronounced as 
frequency increases. In fact there is doubt whether 
the maximum exists at frequencies of 70 and 85 kc. 
Data taken on a second sample indicate a sharp 


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HIGH I'CH^ER DRIVING OF MAGNETOSTRIGTIVE TRANSDUCERS 


.{50 



Figure 35. Variiition in y. and ^ of 0.001-in. SPARS lamination with peak alternating field. 


iipvvard trend of the.'^e two curves in the neigliborhood 
of H equal to 30 oersteds. The curves of reactance 
exliibit even greater differences. At 20 kc the re¬ 
actance increases with H and pas.ses through a 
maximum. For 85 kc it first decreases and then in- 

A 

creases, with H exhibiting a peculiar discontinuity 
between 30 and 60 oersteds. The second sample 
showed only an increase in reactance with H at 
35 kc and confirmed the maximum occurring for the 
20-kc case. The discontinuity shown was definitely 
obser\-ed but it may have resulted from a few pulses 
of current at higher levels, since unit jumps in the 
decade of 10-ohm steps were undoubtedly made 
during the balancing of the bridge. This might have 
altered, through some rectification i)rocess, the 
magnetic state at which measurements were being 
made. In fact, it .seems more surprising that other 
discontinuities were not ob.served than that only a 
single one should occur in the 30 curves of Figure 32. 

On the basis of the eddy-current theory presented 
in Chapter 3 and by neglecting hysteresis entirely, it 
seems rea.sonable to expect the data for the 5-mil case 
to cover a wider range of phenomena. It is the only 
lamination thickness on which measurements were 
made whose critical frequency fc was of such a 
magnitude that xi pa.s.sed through a maximum and 
Xr through a point of inflection within the range of 
measuring frequencies. This, of course, is ba.sed on 


an fc using the initial permeability. For the 1-mil 
case ///<-, on the assumption just noted, did not 
exceed 1.2 and for the 25-mil case it was never less 
than approximately 45. By reference to Figure 1 
of Chapter 3, it is observed that both xi and xn are 
smooth functions approaching limiting values asf/fc 
approaches zero and as f/fc becomes large com¬ 
pared to 2.5. 

Confirmation of the expectance of more complex 
phenomena for the 5-mil case is found in the work of 
Cauer.* He extended the solution of the classical 
eddy-current problem in which the permeability is 
regarded as a constant to a specialized case in which 
n is a variable and B is given by Rayleigh’s ecpia- 
tion, nameh" 

B = (mo + //)// + ^(//■’ - //•’)• 

Here mo i^^ the initial permeabilit}^ H refers to the 
maximum value of //, and a is a constant given by 
the expression 

A (/U — Mo) 
a = M-ic- 

B 

The diacritical mark A refers to the ma.ximum 
value of the quantity. 

Complete solution under the above assumptions 
would involve production of harmonics, but Cauer 
has carried out the solution for the fundamental 


CONFIDENTIAL 









































EXPERIMENTAL STUDA AND DESCRIPTION OF RESULTS 


351 


only. For a-c bridge measurements as made here, 
this is the solution that applies, since filters of high 
discrimination eliminated all harmonics. Legg^* has 
summarized Cauer’s results and it is of interest to 
show that the results presented here for the 5-mil 
case are in qualitative agreement, at least with 
Cauer’s * complicated analysis. He found, for ex¬ 
ample, that the apparent permeability n as calcu¬ 
lated from inductance measurements is given the¬ 
oretically by the expression 


M = 


sinh 6 -f sin 6 
d cosh d -b cos 6 


, 40 -^ 76^ 2e>' 

ocH ^ 1 — — — — -f- 

' Ott 60 457r 


where 6 = 2irl\^unf p with p in emu. This analysis 
predicts that the apparent permealhlity will decrease 
with increasing H for frequencies higher than that 
necessary to make 6 > 1.6 approximately. By assum¬ 
ing 6 — 1.6, p = 8 X 10”'’ ohm cm for nickel, it can 
be found that for any frequency above the one 
given by 


, 8.06 
/ = —7 X 10^ 
Pot- 


in) 


the apparent permeability, or in this ca.se the meas¬ 
ured reactance, will decrease with increa.sing //. For 
the 5-mil example, from the equation above, 
/ = 2.8 X 10^ was obtained. Reference to Figure 
32D shows that at 20 kc the reactance is increasing 
with H up to the maximum, while at 35 kc and higher 
the reactance is decreasing up to peak fields of ap¬ 
proximately 10 oersteds. For the 1-mil example, 
equation (11) yields a value of 920 kilocycles as the 
critical frequency for the change of sign in the slope 
of the reactance vs ajjplied field curve. 

On the other hand, for the 25-mil example the fre¬ 
quency given by (11) is 571 c. This would indicate 
that all the reactance curves of Figure 32F should 
start with a negative rather than a positive slope. 
The thickne.ss of this lamination is roughly a third 
of its breadth, so that the u.sual assumption that the 
thickness is small compared with the breadth is 
probably not justified. This would undoubtedly 
modify the ordinary linear theory of eddy currents 
and probably also Cauer’s extended treatment. 

Figure 33 shows the six families of so-called transi¬ 
tion curves. The family for the resistance of the 
25-mil laminations shows the smoothest transition 
between the types repre.sented by Figures 32 and 34. 
Hysteresis losses are believed to be much more in 


evidence in this type of family than in that of Fig¬ 
ure 32. The areas of the hysteresis loops of Figure 
28 have been found to have the following relative 
values. 

Area 1 mil Area 5 mil 

- = 2 - 555 1.9' 

Area 25 mil ’ Area 25 mil 

The importance of eddy-current los.ses relative to 
hysteresis losses decreases on proceeding from 25 to 
1 mil. Hence the diminution of eddy-current losses 
and the largest hysteresis lo.'^ses combine in the l-rnil 
sample to produce the sharpest rise of resistance as 
a function of H. For 25 mils the eddy-current shield¬ 
ing has certainly greatly reduced the effective volume 
of the nickel, and again hysteresis losses are mini¬ 
mized in this sample and no very marked resistance 
increases are noted. It is also of interest to note that 
the relative change in apparent permeability in B is 
much less than the relative increa.se in resistance, 
again an indication that hysteresis los.ses are most 
important in the 1-mil ca.se. Family D, the 5-mil 
example, again exhibits the most peculiar character¬ 
istics. The apparent permeability as reflected in the 
reactance curv'es first decreases and then increases in 
only two of the five cases, even though the frequency 
is above 28 kc. It would be a difficult matter in these 
hybrid families to know how to calculate the fre¬ 
quency marking the change in initial slope of the 
reactance versus H curve. 

It is believed that this data is of little value beyond 
satisfaction of curiosity as to how one type of family 
merges into the other. If one were interested in the 
detail of electric wave forms, these findings woidd 
probably be of more value. 

Figure 34 .shows the .six families of curves taken in 
each case for a steady polarization Ho to produce a 
magnetic induction Bo of 3,900 gau.sses. The different 
values of Ho to be u.sed for the various lamination 
thicknesses were determined from the magnetization 
curves of Figure 27. The families for the 25-mil 
example display the smallest increments in either 
R or A' with frequency. As noted earlier, eddy-cur- 
rent .shielding reducing the active volume of nickel, 
the inherently small hysteresis loss per cycle in this 
sample, and the very large value of///c for all meas¬ 
ured points combine to bring about the .small changes 
noted. The 5-mil sample shows no marked change in 
sign of the slope of reactance curve. U.sing a value of 
4.8 ohms as the smallest measured reactance at 
20 kc yields an effective permeability of 35. Applying 
this value to equation (11) yields a value for/ of 92 


CONFIDENTIAL 






REACTANCE_IN OHMS RESISTANCE IN OHMS 


352 


men POWER DRIVING OF MAGNETOSTRICTIVE TRANSDUCERS 




0.1 I ^ 10 100 

H IN OERSTEDS 




0.1 I 10 100 

H IN OERSTEDS 


Figure 36. Resistance and reactance at various frequencies of SP.AllS transducer in air as a function of peak alternating 
field. 


A 



2 

X 

o 

2 A 



0 4 8 12 16 20 


A 



A 



A 

H = 40 



A 



0 4 8 12 16 20 


Figure 37. Impedance circles of SP.\RS transducer in air for different constant values of peak alternating field. Ho = 
29 oersteds, t = 0.001 in. 


CONFIDENTIAL 































































































































































































































































































































































































EXPERIMENTAL STLDY AND DESCRIPTION OF RESULTS 


353 



0 12 3 0 12 3 0 I 2 3 4,5 

R IN OHMS 

Figure 38. Data corresponding to Figure 37 hut with transducer in water. 


kc, which on Cauer’s theory is the critical frequency 
for change in sign of the slope of the apparent perme¬ 
ability curve. All measurements, however, were be¬ 
low this frequency. Again, the 1-mil family displays 
very sharp increases in resistance at values of // a 
little in excess of //q. This is believed to result largely 
from hysteresis loss. Evidence of hysteresis effects 
are rather obvious in the stepwise jumps in the re¬ 
actance curves at high values of H and probably 
result from the process of balancing the bridge. 

It is also illuminating to make a study of the total 
angle of lag arising from eddy currents and hystere¬ 
sis. S. Butterworth and F. D. Smith" have shown 
that 


^-^core 

where f and r] are the angles of lag arising from these 


two effects. The total angle ({" rj) may be derived 
from the data .shown in Figures 32, 33, and 34. Only 
a few computations of this angle were made and they 
were in general agreement with what was to be ex¬ 
pected. For the 25-mil sample the angle was always 
greater than 45 degrees, indicating the asymptotic 
value of the eddy-current lag angle in agreement 
with the high value of f/fc. For the 1-mil sample at 
the other extreme, the total angle at low' levels was 
only a few' degrees but rose rapidly in the region 
where H exceeded Ho in the polarized case. 

Much more may be done tow'ard interpretation of 
the data by Cauer’s theory and the aim here has been 
to present the data in sufficient detail so that any¬ 
one interested may carry out additional computa¬ 
tions. There has been no opportunity to attempt to 
separate the losses by standard methods such as 


CONFIDENTIAL 































































































































































HIGH POWER DRIVING OF MAGNETOSTRICTIVE TRANSDUCERS 





Figure 39. Modified iircssure chamber. 


outlined by Legg. It is believed at least that at the 
lower levels his methods should apjily. Then perhaps 
Cauer’s work will be useful at slightly higher fields, 
though it is probable that as yet no adequate theory 
has been developed for the highest levels. 

After the data were taken with the three test cores 
wound tightly with 70 turns of wire, they A\ere each 
unwound and reassembled with pressure-release ma¬ 
terial isolating the nickel stacks between fiber rings. 
Windings of 60 turns were then put on to make a 
typical ring stack transducer as described in Chapter 
6. The 60-turn winding was tried out on the 1-mil 
stack and sufficient data taken to obtain vector im¬ 
pedance loci by sectioning runs made at constant 
frequency. 

This procedure was exactly similar to that used 
earlier in connection with the STEP element. Curves 
of resistance and reactance as a function of peak- 

A 

applied alternating field (H) are shown in Figure 36 
for each of eleven different frequencies. These data 
were taken with the stack in air. For six constant 

A 

values of H, resistance and reactance values were 
read from the cur\'es; the six vector imiiedance loci 


are shown in Figure 37. This example reflects the 
maximum motional effects. Figure 38 is similar to 
Figure 37 except that the stack was submerged in 
water and the overall effects here include that of 
loading. Data for Figure 38 were, of course, taken 
from a series of curves analogous to tho.se shown in 
Figure 36. By use of the data from Figure 34 in 
conjunction with that of Figure 36 and by the best 
possible estimation of the leakage inductance, it is 
probable that a rea.sonable separation of purely mo¬ 
tional resistance and reactance could be made. If 
this were done, deviations from the predictions of 
small signal impedance data would be obtained. Un¬ 
fortunately, lack of time prevented this analysis. 

Finally it may be of interest to note that the pres¬ 
sure container shown in Figures 8 and 9 was not 
suitable for acoustical measurements on ring stacks. 
The vessel and stack mounting shown in Figure 39 
was devised, having symmetry about its vertical axis. 
Here perforated metal was used to prevent the bulg¬ 
ing of the rubber .side walls under pressure. Prac¬ 
tically no acoustical measurements were made with 
this device and the question of polarized driving ver- 


CONFIDENTIAL 







CONCLUDING COMMENT 


355 


sus hali-frequency driving with no polarization had 
to be deferred for the ease of ring stacks. The type of 
mounting, however, illustrates a useful construction 
for further work. 

11.6 CONCLUDING COMMENT 

It should again be emj)hasized that the material 
presented here represents a general survey of the 
phenomena to be encountered and of the problems 
ari.sing in the field of high-level operation. It is not a 
precision study. In extending the matter further it is 
suggested that a rather critical appraisal of the data 
presented .should be undertaken first. Accompanying 
this .should be a thorough study of the theoretical 
work that has been published to date in this general 
field. It is believed that the partial quantitative 
agreement with certain of Cauer’s results justifies this 
point of view. Specific power lo.sses in nickel may be 
calculated approximately from the data presented in 
Figures 32 and 34. The data of Figures 37 and 38, 
coupled with that of Figure 34, should allow the 
.separation of the purely motional part of the vector 
impedance loci. A comparison of the air and water 
circles at the various constant levels should then indi¬ 


cate the trend with level of all properties derivable 
from motional impedance data. This study shoidd 
jmovide evidence concerning the utility or lack of 
utility of impedance data at high levels. 

The phenomena of nonpolarized half-frequency 
driving certainly merits more exhaustive study, both 
theoretical and experimental. The rapid decrease of 
the resistance in the high-field region where acoustic 
output and efficiency are both increasing should be 
investigated further. Experimental investigation 
should be made of the possibilities of nonsinusoidal 
driving currents, since the idealized theory points 
definitely in this direction. References have been 
cited to other nonlinear problems which also support 
this view. In fact, it is suggested that a careful study 
of the complex wave forms encountered in high-level 
driving should be carried out to ascertain definitely 
the part played by source impedance. For this pur¬ 
pose the development of a power amplifier with ad¬ 
justable internal impedance and higher output power 
should be carried out. Similarly a reliable recording- 
pulse voltmeter with logarithmic scales would greatly 
facilitate the experimental work. Such an instmment 
should if po.ssible have the reliability of the w^ell- 
known Ballantine electronic voltmeter. 


CONFIDENTIAL 




Chapter 12 

FUTURE DEVELOPMENTS 


12.1 MAGNETOSTRICTIVE MATERIAL.S 

12.1.1 New Materials 

The ideal material for magnetostrictive tran.sdueers 
would have high coercive force, high reversible per¬ 
meability, high remauence flu.x density, high con¬ 
stant of magnetostriction, high electric resistivity', 
and relatively low cost. It should be capable of being 
rolled, punched, or formed into accurate shapes. It 
should have uniform mechanical and chemical ]3rop- 
erties. A material having the characteristics shown in 
the second column of Table 1 could be used to make 
a tran.sducer which would be nearly ideal. 


T.\ble 1. Characteristic values for ideal and various 
currently used magnetostrictive materials. 


Property 

Ideal 

material 

(approx¬ 

imate 

values) 

.\nnealed 

nickel 

Semi- 

annealed 

nickel 

.\nnealed 

45-Per¬ 

malloy 

Semi- 

annealed 

2V-Per- 

mendur 

He 

100 

4 

25 

0.32 

25 

(oersteds) 






Br 

5,000 

1,400 

3,000 

10,000 

17,000 

(lines/cm-) 






Mr (at Br) 

100 

SO 

18 

800 

50 

X (at Br)* 

2x10’ 

0.7x10' 

1.1x10’ 

0.22x10’ 

1.1x10' 

Pr 

10-’ 

10x10-" 

10x10-" 

.54xl0-« 

39x10-" 

(ohm/cm) 






p 

3 

8.9 

8.9 

8.3 

8.2 

{(j/cm^)i 






E 

5x10“ 

2.10x10'= 

2.2x10’= 

1.4x10'= 

2.15x10'= 

(dynes/cm^) 






vt 

0.005 

0.013 

0.030 




^Magnetostriction constant. 

tDensity. 

^Coefficient of magnet hysteresis loss (as in energy loss j)er cycle = 

A transducer made of a material like this, which 
could be made to have a (J of 2 and a ma.ximum effi¬ 
ciency of about 80 per cent, woukl need no polariza¬ 
tion other than the magnetic remanence. Unfortu¬ 
nately, some of the t allies given above are naturally 
incompatible. For instance, high coercive force and 
high reversible permeability are natural opposites. 


The .same is generally true of coercive force and the 
coefficient of magnetic hysteresis. Consequently, the 
development of new magnetostrictive materials must 
be in the direction of finding favorable compromises 
among the various sets of characteristic values. 

The values for several current 1}^ used magnetostric¬ 
tive materials are given in Table 1. At present, 
2V-Permendur is the best magnetostrictive material 
for use at magnetic remanence at reasonably high 
power levels. In the most efficient geometrical form, 
i.e., in laminated ring stack, 2\'-Permendur can be 
made to give efficiencies up to 50 per cent and rms 
pressures of about 10® dynes per .sq cm at a me¬ 
chanical Q of about 6 when operating at magnetic 
remanence. Due to the trends toward high power 
transmitting it is desirable to have a magnetostric¬ 
tive material capable of giving acoustic pressures of 
the order of 2 X 10® to 5 X 10® dynes per sq cm 
when operating at magnetic remanence and at me¬ 
chanical Q’s of the order of 6 to 12. The material 
should not be prohibitively exjiensive, as 2V-Per- 
mendur is at .$8.30 per lb. 

If a material could be found that has all the ideal 
jiroperties suggested except the high coercive force, 
it could still lie used very satisfactorily in many de¬ 
signs liy' polarizing it with permanent magnets or 
with direct current in the windings. 

12.1.2 New Techniques in Making 
and Treating Alaterials 

Rolling, Sintering Powders, Electroplating 

The magnetic and magnetostrictive properties of 
some metals and alloys can be influenced to a con¬ 
siderable extent liy the degree of cold-working to 
which they are subjected before heat treatment. 
Sometimes the direction of rolling produces definite 
orientation effects which are quite desirable for use 
in certain types of elements, ('onsequently in the 
development of new materials not only new alloys 
but different methods of mechanical preparation and 
heat treatment should be tried. 

The idea of making magnetostrictive transducer 


356 


CONFIDENTIAL 


















PERMANENT MACiNET MATERIALS 


357 


elements by consolidating powdered magnetostrictive 
metals in accurately formed molds (in about the 
same manner as consolidated powder transformer 
cores are made) is very attractive because of its in¬ 
herent simplicity. Some experiments of this type, in 
which powdered nickel and powdered 45-Permalloy 
were used, have been tried without success. In a 
material thus formed, the electric contact between 
particles must be small, the Young’s modulus large 
and uniform, and the internal friction nearly as small 
as that in a solid metal. The samples made u]) to the 
date of this writing have shown only very small mag¬ 
netostriction and rather high internal friction. It is 
possible that proper methods of powdering, con¬ 
solidation, and heat treatment could result in a satis¬ 
factory material. The advantages of such a material, 
compared with the conventional stacks of lamina¬ 
tions, would justify the expenditure of a considerable 
amount of time and effort to develop it. 

Forming magnetostrictive elements by electro¬ 
plating has some attractive advantages over other 
methods, especially if the material could be deposited 
in layers, with considerable resistivitj^ between the 
successive layers. Some experiments have been per¬ 
formed along this line without very much success. It 
was found that semiconducting layers of oxides or 
sulfides covering the previously deposited layer of 
nickel did not have enough conductivity and did not 
provide a proper base for the deposition of the next 
layer. The magnetostrictive quality of the nickel so 
deposited was found inferior to that of rolled nickel 
sheet that has been properly heat treated. However, 
the pos.sibility of forming laminated tubes or plates 
by electroplating magnetostrictive material is inter¬ 
esting and the advantages it offers make further con¬ 
sideration and experimentation worth while. 

Heat Treatments 

(Much work has been done in the past in determin¬ 
ing the effects of various heat treatments on the 
magnetic and magnetostrictive i)roperties of metals. 
This is particularly true of nickel, 45-Permalloy, and 
2\’-Permendur. The residts of this work show that 
the initial structure of the metal, the temperature, 
the time, and the atmosphere in which the annealing 
is done all affect the result. It is also known in a 
general way that heat treating in a magnetic field can 
influence the magnetic and magnetostrictive proper¬ 
ties of the material. On the basis of the magnetic 
domain theory of magnetism, it can be shown that 
the magnetostriction of a sample with all its domains 


oriented transverse to the final field direction by heat 
treatment in a magnetic field should be % times that 
of a sample of the same material whose magnetic 
domains are oriented at random. Very little experi¬ 
mental work has been done along this line. The 
jiossible gain in magnetostrictive properties indi¬ 
cates that further work would be worth while. 

12.2 PERMANENT MAGNET MATERLALS 

It has been shown in previous chajjters that when 
the return paths of the polarizing flux and the high- 
frequenc}^ dux are separate, magnets made of some 
of the Alnico alloys can be used to provide the po¬ 
larizing dux. This is especially true of those trans¬ 
ducers in which there is adequate space between the 
vibrating elements for the relatively bulky magnets. 
In such cases it is good practice to shield out the 
high-frequency dux from the Alnico magnets to pre¬ 
vent lo.sses due to eddy currents. The Alnico alloys, 
naturally very l:)rittle materials, must be cast in 
relatively thick sections and consequently cannot l)e 
laminated to minimize eddy-current losses. Neverthe¬ 
less it is economical and practical to use the com¬ 
mercial varieties of Alnico magnets in certain types 
of magnetostrictive transducers. 

There are many cases in which the space available 
for the transducer elements is so limited that there 
is not sufficient room for polarizing magnets out.side 
the element itself. In these cases it is convenient and 
practical to include the polarizing magnet in the 
high-frequency dux path. Polarizing magnets so used 
should occupy the smallest possible fraction of the 
length of the high-frequency dux path i^o as not to 
increase the reluctance of the high-frequency mag¬ 
netic circuit more than is absolutely necessary. The 
polarizing magnet material should, therefore, have a 
^'ery high coercive force, even at the expense of dux 
density. To minimize losses due to eddy currents 
and eddy-current shielding, the permanent magnets 
used as part of the high-frequency magnetic circuit 
shoukl have a very high resistivity or be laminated 
or both. Such magnets should also have as high a 
reversible permeability as is consistent with the re- 
ciuired large coercive force. The material of this type 
which has proved best up to the time of this writing 
is sintered iron oxide (Vectolite), a permanent mag¬ 
net material made by the General Electric Company. 
Although sintered iron oxide is satisfactory in most 
respects, it would be better if it coidd be made to 
have a higher coercive force, a greater remanence 


CONFIDENTIAL 



FUTI RE DEVELOPMENTS 


3.>8 


Hux density, and a greater permeability for high- 
frequency flux. The ideal permanent magnet ma¬ 
terial for use in polarizing tran.sducer elements by 
inserting the magnet in the high-frequency magnetic 
path should have the following approximate char¬ 
acteristics; 

1. He ^ 1,000 oersteds. 

2. Br ^ 2,000 lines per sq cm. 

3. Pf ^ 10^'^ ohm-cm. 

4. pr ^ 5. 

5. Negligible magnetic hysteresis lo.ss. 

6. Should be capable of being formed or molded 
to accurate mechanical dimensions. 

7. Should maintain nearly its full coercive force up 
to temperatures as great as 250 F. 

It is po.ssible that some material similar to sintered 
oxide could be developed that wovdd have the proper¬ 
ties listed above. It is al.so possible that some metallic 
alloy with the desired properties might be developed. 
It would be practical to compromise on a lower value 
of resi.stivity if the material had, in addition to all 
the other properties listed, the property of malle¬ 
ability, .so that it could be rolled into sheets thin 
enough to make the eddy-current losses very small. 

12.3 RADIALLY VIBRATING RINGS 

12.3.1 Conventional Ring Stacks 

Construction of Stacks 

Satisfactory methods of punching and heat-treat¬ 
ing ring-shaped laminations have already been dis¬ 
cussed in Chapter 6. The new types of design and 
construction suggested below may be of interest in 
special applications. 

The method usually employed to reduce the me¬ 
chanical Q of a ring stack is to decrea.se the ratio of 
wall thickness to mean radius. This automatically 
decreases the crushing .strength of the ring stack. 
A method of reducing the Q without decreasing the 
strength of the walls is to intersperse rings of alumi¬ 
num, magnesium, or their alloys between rings of 
magnetostrictive matei'ial. In rings made of the light 
alloy the velocity of sound should be very nearly the 
same as that in the magnetostricti\'e rings l)ut their 
mass is much le.ss. Mixing the two types of lamina¬ 
tions causes an increa.se in radiation resistance, with¬ 
out a proportionate increase in the ma.ss of the vi¬ 
brating parts, and a consequent lowering of the Q. 
The electromechanical efficiency would be decreased 


by about the .same amount as that of a stack com¬ 
posed entirely of magnetostrictive material but hav¬ 
ing a wall thickne.ss with the same mechanical Q as 
the composite stack. 

The problem, never so far satisfactorily solved, of 
polarizing ring stacks made of magnetically .soft mag¬ 
netostrictive materials could be resolved by using the 
permanent magnet material propo.sed in Section 12.2 
as a magnet extending across the diameter of the 
stack. This magnet would be surrounded })y a wind¬ 
ing and would furnish a return path for the high- 
frequency flux as well as provide the polarizing flux. 

When the laminations of a ring stack are firmly 
bonded together, mechanical coupling between the 
longitudinal and radial modes of vibration sometimes 
cau.ses trouble. This trouble generally occurs when 
the natural frequency of one of the longitudinal 
modes of vibration is nearly equal to that of the 
radial mode of vibration. Troubles of this kind might 
be eliminated by breaking the .stack into longitudinal 
segments, with laminations of corprene or air-cell 
neoprene cemented between the segments. The height 
of the segments would be determined by the size of 
the rings and the frequency at which they are to be 
operated. 

Methods of Mounting and Housing 

Many methods of mounting and housing ring-stack 
transducers have been developed to fit the specific re- 
ejuirements of difTerent jobs. One of the most common 
uses of ring stacks is in echo repeaters, where the 
electrical, mechanical, and acoustical coupling be¬ 
tween the transmitting and receiving transducers 
must be kept at a minimum. Nearly all the designs 
for echo repeaters have u.sed ring stacks in isolated 
mounts, hou.sed in rubber tubes and filled with castor 
oil. This type of construction is inherently compli¬ 
cated and expensive. Some further development work 
in the direction of simplifying ring-stack housings 
anil water seals for echo repeaters and similar de¬ 
vices is indicated. 

The design and construction of conventional singly 
mounted ring stacks used as monitors or as noise 
sources have been described in detail in Chapter b. 
These mountings and hoti.sings are quite .simple and 
rtigged and improvements will be mainly in minor 
details. 

An tinti.sual method of winding and housing a ring 
stack, illustrated in Figure 1, was suggested lait never 
tried. In this design the copper case also serves as the 
.single-turn toroidal winding of the ring stack and the 


CONFIDENTIAL 



RADIALLY VIBRATING RINGS 


339 


enclosed transformer. The cable leads are attached 
to the terminals of the enclosed transformer’.s sec¬ 
ondary winding, which has the proper number of 
turns to give the desired impedance for the device. 
Acoustic contact between the outside wall of the 
housing and the ring stack can be made by using 



RESIN OR PLASTIC 
FILLING BETWEEN 
RING STACK AND 
CASE 


COPPER CASE 
SERVES ALSO AS 
SINGLE - TURN WIND 
ING FOR RING STACK 
AND PRIMARY WINDING 
CF THE TRANSFORMER. 


metal tube mousing 

FOR plastic cable 

seal 


TRANSFORMER CORE 
(COMPRESSED DUST 
OR LAMINATED) 


secondary winding 
OF TRANSFORMER 


RING STACK OF 

MAGNETOSTRICTIVE 

LAMINATIONS 


PRESSURE RELEASE 
MATERIAL COVERING 
TOP, BOTTOM a INSIDE 
SURFACES OF RING STACK 


Figure 1. design for a ring-.stack transducer in which 
the ca.se serves as a single-turn toroidal winding. Any 
desired output impedance is obtained by use of the self- 
enclosed transformer. 


some type of pla.stic or liquid filling free from any 
gas bubbles or voids. These units are rugged, simple, 
and easy to manufacture. They could be readily 
adapted for u.se with radio sono buoj^s, echo repeat¬ 
ers, noise .sources, etc. They should be able to with¬ 
stand submersion to great dejTths without danger of 
crushing or leaking. 


12.3.2 Solid-Walled Tubes 

Solid-walled tubes can be wound toroidally .so that 
the magnetic fiux is circumferential, or a core piece or 
polarizing magnet can be inserted across the diam¬ 
eter with a coil surrounding it .so that the flux path 
extends acro.ss the tube parallel to the diameter and 
returns circumferentially through the two halves of 
the magnetostrictive tube {B-19 type). The toroidally 
wound type is inherently more efficient because the 
high-frequency flux remains within the tube wall, 
whereas in the second type the flux must enter and 
leave the tube walls at the opposite ends of the 
diameter. Both these types have been developed to a 
considerable degree of perfection. There is no ob¬ 


vious way of making any marked improvements over 
the pre.sent forms until new magnetostrictive ma¬ 
terials are developed that have sufficient coercive 
force and remanence to make po.ssible the construc¬ 
tion of toroidally wound tubular units that can be 
operated at reasonably high power levels at magnetic 
remanence without danger of demagnetization. A ma¬ 
terial that nearly meets the magnetic and magneto¬ 
striction requirements is 2V-Permendur but whether 
or not it can be drawn into tubular form is question¬ 
able. Also, it is almost prohibitively expensive. 


12.3.3 Flat-Wound Scrolls and 

Layer-Built Tubes 

Consolidation 

Flat-wound scrolls and layer-built tubes or rings 
(layer-built tubes are made of discrete layers of 
laminations, like an onion) are superior to solid- 
walled tubes or rings in that the eddy-current lo.sses 
are less because of the lamination effect. However, 
when these are used as radial vibrators, pressure 
must be tran.smitted from layer to layer uniformly 
and without lo.ss. It is, therefore, neees.sary that all 
the voids between succe.s.sive layers be completely 
filled with solid bonding material. A great amount of 
development work has been done at the Bell Tele¬ 
phone Laboratories and at Harvard on methods of 
producing sati.sfactory impregnation and bonding of 
transducer cores of this type. Only moderate success 
has been attained. The economical use of magneto¬ 
strictive material and the flexibility of design which 
are characteristic of this method of making rings and 
tubes make it worth while to continue re.search on 
methods of consolidating the layers perfectly. In ad¬ 
dition to giving good adhesion and mechanical con¬ 
tact between successive layers of laminations, the 
method should also leave the lamination layers prop¬ 
erly heat-treated and free of mechanical strains which 
detract from the optimum magnetic and magneto¬ 
strictive performance. 

Polarization 

The lamination effect of ring-shaped scrolls or 
layer-liuilt rings can be utilized only if the magnetic 
circuit is purely circumferential. This means that the 
polarizing flux mu.st be maintained by the use of a 
component of direct current in a toroidal winding or 
that the material must be operated at its magnetic 
remanence. Polarizing current is undesiralile becau.se 
of all the auxiliary etiuipment it entails. The best 


CONFIDENTIAL 



































FUTURE i)p:veuopments 


:}6() 


solution to the prol:)lem is the development of a mag;- 
netostrictive material that can be operated with high 
efficiency at high power levels at magnetic remanence 
without danger of depolarization. 

12.3.1 Edgewise-\^ ound Tape to 

Form Tubes 

Stacks of ring-shaped laminations make the most 
nearly ideal radial magnetostrictive vibrators, flow- 
ever, the production of such ring laminations wastes 
magnetostrictive material, since the rings must be 
punched from fiat sheets. This waste may be elimi¬ 
nated by making the tubes or rings by edgewi.se wind¬ 
ing of narrow tape made of magnetostrictive metal. 
The width of the tape should be very nearly equal to 
the desired wall thickness of the final tube or ring. 
After the tape is wound it should be consolidated 
with a resin to form a firm solid-walled structure. It 
appears that this method coidd be applied particu¬ 
larly well to the construction of relatively thin-walled 
tubes. Some e.xperimental work on this method has 
been pursued at HUSL but without much success. 
The samples made showed lower permeability and 
higher internal mechanical damping than ecpiivalent 
ring stacks of standard construction. There is no 
reason to believe, however, that the difficulties can¬ 
not be overcome by development of the projjer 
techniques. 

The problem of polarizing rings or tubes of this 
type is the same as for standard laminated ring 
stacks. 

I2.t LONGITUDINALLY VIBR.\TLNG 
LAMINATED STACKS 

12 . 1.1 Conventional Forms — HP 

and SP Types 

Most of the problems involved in making con¬ 
ventional punchings have been solved in one way or 
another. Very good dies are required to punch lami¬ 
nations from thin, tough nickel sheet without the 
formation of bad burrs at the edges. Some im])rove- 
ments coidd be made in methods of collecting lami¬ 
nations from the punch pre.ss, cleaning them, and 
annealing them. Several reasonably successful meth¬ 
ods of consolidating laminations into stacks have 
been developed and described. However, problems 
keep arising in the production of laminated stack 
transducers which indicate that considerable im¬ 
provement could be made in the methods. 


The design of laminations of the HP and SP types 
proved to be quite .satisfactory. It has been suggested 
that laminations might be modified in shape and 
size so that two frequencies of re.sonance fall close 
enough together with the proper degree of mechanical 
coupling to obtain a fiat frequency response over a 
short frequency interval. This result was obtained 
accidentally in the laminations of the HP-1 tran.s- 
ducer. Also, experiments have been made by build¬ 
ing stacks made up of .short .stack segments of slightly 
different lengths. Broadened frequency respon.ses 
have been obtained by these methods but always at 
the expense of maximum efficiency. Further sys¬ 
tematic inve.stigation of this effect would be of 
theoretical interest and possibly of some practical 
importance. 

Methods of supporting and mounting laminated 
stacks in a more rugged and efficient manner should 
be developed. This is particularly true of those trans¬ 
ducers that must be subjected to great mechanical 
shocks and stre.sses. Many new methods have already 
been proposed in the preceding chapters. 

12 . 1.2 Bookphone Type 

The original bookphone described in Chaiiter 7 did 
not proi'e to be of practical importance because of 
difficulties involved in attaching the ends of the 
booklike laminated stacks to the diaphragm plates 
and becau.se of the imperfect high-frequency mag¬ 
netic circuits. Experience gained in design and tech¬ 
niques since the bookphone type of tran.sducer was 
first investigated indicates that a practical and ef¬ 
ficient transducer of this type could now be made. 
However, about the only advantage of the book¬ 
phone type over the HP or SP types is that the lami¬ 
nations can be made without any waste of material. 

12.5 TIBE-AND-PLATE TRANSDUGERS 

Tube-and-plate type transducers are perhaps the 
oldest and the best developed type of magnetostric¬ 
tive tran.sducers. The QC series of sharp-beam echo¬ 
ranging transducers used by the Navy for years have 
demonstrated their ruggedness, stability, and prac¬ 
ticability. The (^C series of tran.-^ducers have mod¬ 
erate efficiencies because of their relativ'ely high me¬ 
chanical O’s. Some of the later models are polarized 
with permanent magnets so that no auxiliary equip¬ 
ment is needed for polarizing current. 

Improvements most needed in transducers of this 
type are lower mechanical Q's and higher efficiencies. 


CONFIDENTIAL 



IMULTIELEIMENT CYLINDRICAL TRANSDUCERS 


361 


Much experimental work has been clone in this line 
by Peek of the Bell Telephone Laboratories. By use 
of thin-walled annealed nickel tubes and a diaphragm 
of magnesium alloy, Peek was able to make a trans¬ 
ducer which is about 10 per cent efficient at a me¬ 
chanical Q of 10. This is about as high an efficiency 
as can be obtained with a tube-and-plate type of 
transducer at this Q. There is some ciuestion, there¬ 
fore, as to whether much time should be spent in 
developing further details of the tube-and-plate type 
of transducer when transducers of lower Q, greater 
efficiency, and ecpial ruggedness can be made with 
laminated-stack elements. The chief jn-actical argu¬ 
ment in favor of the use of tube-and-plate tran.s- 
ducers is that they use much less magnetostrictive 
material than do the laminated stack types. 

If tube-and-plate type elements of relatively high 
are to be developed for use in multielement trams- 
ducers, where the elements must match each other 
closely in phase, methods must be found for match¬ 
ing the frequencies of the individual elements within 
very close tolerance. 

12.6 MULTIELEMENT CYLINDRICAL 
TRANSDUCERS 

12 . 6.1 General Strength and 
Ruggedness 

Most of the multielement cylindrical transducers de¬ 
signed and constructed have been reasonably strong, 
rugged, and satisfactory for operation down to depths 
of the order of 400 to 500 ft of water. It is desirable, 
however, to make transducers that will withstand at 
least twice these external pressures in order to with¬ 
stand depth charges and deep submersions Avithout 
breaking down. Improved methods of making cast 
or forged frames for these large transducers should 
be developed because much trouble has been experi¬ 
enced with porous places in the metal castings. At¬ 
tention should also be paid to chemical corrosion 
resistance of exposed parts of the transducers. 

There are some advantages in housing the ele¬ 
ments of a cylindrical transducer separately in 
watertight containers easily removable from the main 
frame of the transducer. All developments in this di¬ 
rection have so far been unsuccessful. If the advan¬ 
tages of removable separate elements are deemed 
great enough, more development work along this line 
should be done. 

It is difficult to make .satisfactory cable seals for 


the large cables needed for multielement trans¬ 
ducers on submarines. The seals should be designed 
to hold .satisfactorily at water pressures as great as 
500 or more lb per sq in. At pressures as high as these, 
the cables tend to extrude through the water .seal. In 
the design of new water seals, attention should also 
be paid to the ease with which the seal can be taken 



A TYPE THAT IS EASILY TAKEN APART 



THREAD CUT TOO 
DEEP, GASKET 
STICKS IN THREADS 


B TYPE THAT IS VERY DIFFICULT TO TAKE APART 


Figure 2. Two cable seals which have equally good 
■sealing qualities but widely different disassembly 
characteristics. 


apart after it has been a.ssembled for a long time. 
To illustrate this Figure 2 shows two large cable 
seals with ecpial sealing powers. The one shown in A, 
however, can lie taken apart much more easily than 
the one shown in B. 

Most of the water seals between flanges and plates 
of large transducers make use of rubber gaskets in a 
tongue-and-groove assembly. In this type of seal it 
is common practice to leave 0.015 in. or more clear¬ 
ance between the tongue and the groove wall on the 
water side of the gasket in order that the excess 
rubber of the gasket can extrude between the tongue 
and the groove when the two flanges are bolted down 
tight, metal to metal. This method has been quite 


CONFIDENTIAL 































362 


FUTURE DEVELOPMENTS 


suecesst'ul. Another successful type of seal uses a 
rather close-fitting tongue-and-groove with a cor- 
prene gasket. The corprene gasket is made with di¬ 
mensions giving it a volume about 10 per cent greater 
than the closed volume of the tongue-and-groove 
gasket chamber. The compre.ssibility of the cork 
particles in the corprene gives the gasket resilience so 
that the .seal remains tight regardless of temperature 
changes and aging. 

Most sonar tran.sducers have rubber parts which 
are exposed to the .sea water, mineral oil, grease, 
etc. When on topside-mounted transducers on sub¬ 
marines, the rubber is also sul),iected to the action 
of .sunlight and air. The rubber used for such parts 
should be as highly resistant as possible to the agents 
just listed and .should be, in addition, acoustically 
transparent and mechanically strong and tough. The 
pc rubber developed for the Navy by the Goodrich 
Rubber Company has most of the characteristics 
mentioned except high mechanical strength and re- 
.sistance to decompo.sition by the action of sunlight. 
Further development work should be done toward 
making a rubber or rubber-like material which has 
all the desirable characteristics li.sted above. 

Transducers must often be mounted in ])laces 
where .surfaces in the vicinity of the transducer give 
troublesome reflections of .sound. These reflection 
troubles could be greatW reduced if the reflecting 
surfaces could be covered with some rul)ber-like ma¬ 
terial which has a pc nearly equal to that of water 
and a ^•erv high coefficient of absorption. Butyl rub¬ 
ber more nearly fills the.se refiuirements than any 
other generally known type, but it is not good enough 
at the usual sonar frequencies. The development of 
a better material of this type would be very worth 
while. 

12 .6.2 Cost of Production 

The cost of producing magnetostrictive multi¬ 
element tran.sducers of the laminated .stack type 
which had been completed before the time of this 
writing range upward from about .$8,000 each. Of 
this amount, about .$1,200 is required to purcha.se the 
nickel strip material from which the laminations are 
punched. This amount cannot be reduced unless the 
price of nickel is reduced. It is believed that in 
routine production, by use of good manufacturing 
economjq the cost of tran.sducers of this type could 
be brought down to about $.5,000 or $6,000. 

The cost of the nickel used in a tube-and-plate tyjie 


of multielement tran.sducer would l)e almost insig¬ 
nificant, but the labor cost of the manufacture of the 
multiplicity of small accurate parts would still be 
quite high, so that the total cost would be about 
$5,000. 

12.6.3 Noiicircular Transducers 
for Eliminating Domes 

When the conventional cylindrical-shaped multi¬ 
element transducer is mounted on a .ship that can 
travel at speeds greater than 10 or 12 knots, the 
transducer must be surrounded by a streamlined 
dome which is acoustically transparent in the regions 
where the main acou.stic beam of the transducer 
strikes it. The streamlined dome is nece.s.sary to pre¬ 
vent turbulence and cavitation of the water around 
the transducer. It has been suggested independently 
by various persons that the necessity for a dome 
might be eliminated if the shape of the transducer 
itself be an approximately streamlined form. If the 
active faces of the elements should be made to fall 
on .such a streamlined contour, each element would 
have to be equii)ped with an electric delay section so 
that the electric signals would be phased as if they 
had come directly from elements mounted on a 
cylinder. 

Another way of acconi))li.shing the same result 
would be to mount the elements .so that their active 
faces fall on a cylinder and to make the transducer 
case in a streandined form. This would l)e equiva¬ 
lent to building the dome on the tran.sducer rather 
than on the ship. 

12 . 6.1 Submarine Types 

Tran.sducers used on .submarines must be capable 
of withstanding greater external hydraulic pressures 
and greater shock wave pressures than those used on 
surface craft. If submarines are intended to go to 
depths of 1,000 ft, the transd ucer must be capable of 
withstanding static hydraulic jiressures of 450 lb per 
s(i in. and should be able to withstand twice that 
amount in order to have a rea.sonable factor of .safety. 
The tran.sducer must also be capable of withstanding 
impidsive pressures as great as the submarine itself 
will withstand. These recjuirements make it necessary 
to design all parts of the transducer frame .stronger 
than those for use on surface craft. These require¬ 
ments also make it necessary to design and construct 
the vibrating elements of the transducer so that they 


CONFIDENIIAL 



IlIGH-POWER TRANSDUCERS 


Mi 


will not collapse or become inoperative when sub¬ 
jected to large hydraulic pressures. 

It has been found that laminated stacks of the HP 
type have strength enough to withstand compressive 
loads of 2,000 or more lb per sq in. pressing on the 
active faces. However, in this type of construction 
there are two weak places. The first is the small gap 
between the active faces of neighboring stacks 
where the rubber boot is not supported. High 
external hydraulic pressures cause the rubber boot 
material to extrude into the gaps between the 
elements. Under extreme conditions this would cut 
the boot and cause trouble. The second weak point 
is at the back faces of the laminated stacks where 
the stacks rest against the cushioning material on 
the spool core. If the laminated stacks contain 
magnet slots, the bearing area at the back end of 
the stack is only about 0.4 that of the front face. 
Consequently, the bearing pre.ssure of the back 
faces of the stacks against the cushioning material 
is about 2.5 times the pre.ssure on the active face. 
Thus, for pressures of the order of 500 lb per sc] in. 
on the active face, the pressures exerted by the 
back faces against the cushioning material are of 
the order of 1,250 lb jier sq in. Such pressures are 
sufficient to crush or deform most cushioning ma¬ 
terials, especially if the layer is very thick. Conse¬ 
quently, the cu.shioning material will be forced into 
the magnet slot and the gaps between neighboring 
stacks. This trouble can be decreased to .some extent 
by placing a strip of bakelite, laminated glass fiber, 
or aluminum between the back faces of the stacks 
and the layer of cu.shioning material, so that there 
is a greater bearing area and no open gaps into which 
the cushioning material can extrude. However, when 
material of appreciable mass is added to back faces 
of the stacks, undesirable freciuency changes may 
result. Consequently, the material should be .small in 
ma.ss, stiff, and uniform. A considerable amount of 
research work should be done toward finding or de¬ 
veloping better cushioning (i.e., pressure-relea.se) ma¬ 
terials which will withstand great static pressures 
without permanent deformation and without losing 
their pre.ssure relea.se or cushioning properties. Also, 
some methods should be worked out for properly 
supporting the rubber boot over its entire inner sur¬ 
face. The most obvious method would be to extend 
the faces of the laminated stacks so that the gap be¬ 
tween the edges of the faces would be too small to 
allow extrusion of the rubber boot material. This 
would entail some other difficidties, however. 


The problem of making trustworthy cal)le seals for 
tran.sducers used on submarines is somewhat com¬ 
plicated. This problem should be given further ex¬ 
perimental study and improved forms of .seals should 
be developed. 

12.7 HIGH-POWER TRANSDUCERS 

When underwater-sound echo-ranging .systems are 
used on high-sjjeed vessels, the noise level produced 
in the water by the ship is so high that the intensity 
of the echoes must be relatively high to be detected 
above the noise. In this ca.se the best method for in¬ 
creasing the signal-to-noise ratio is to increase the 
signal strength. This can be accomplished by in¬ 
creasing the strength of the initial ping. The only 
limitations to the ultimate power levels that can 
be reached are the ability of the water to transmit 
the power without cavitating and the ability of the 
transducer to convert electrical power to mechanical 
jjower without breakdown or saturation. 

It has been found that the acoustic pressure may 
be increased to several times the local hydrostatic 
pre.ssure in water if the periods of transmission are of 
(piite short duration. For exainjile, if the transmis¬ 
sion periods are made as .short as one millisecond, the 
acoustic i)ressure may be made many times as high 
as atmospheric pre.ssure without trouble from cavi¬ 
tation. 

The upper power limit on magnetostrictive tran.s¬ 
ducers is set l)y magnetic saturation of the magneto¬ 
strictive material and by the efficiency of the trans¬ 
ducer elements. It has been shown (Chapter 11) that 
the upper limit to the mechanical power which can 
be produced l)y annealed nickel is about Qmf, o watts 
])er cu cm of active nickel. In radially vibrating ring 
stacks the entire volume of nickel is fully active, 
whereas in the tubes of a tube-and-plate tran.sducer 
or the legs of the HP type of laminated .stacks only 
about one-half of the actual volume of nickel approxi¬ 
mates full activity. The amount of this available 
mechanical power which is converted into acoustical 
power in the water is determined l)y the mechanical 
efficiency of the unit. 

It is estimated from actual measurements at lower 
power levels that the maximum acoustic pre.ssure 
that can be produced in water at the active face 
of the 26-kc HP-3 type cylindrical transducer is 
about 3 or 4 X 10’’ dynes per sq cm (20 to 30 watts 
per sq in.). This is at a of approximately 10. If the 
laminations .should be redesigned to give twice this Q,, 
then the maximum acoustic jjower output could be. 


CONFIDENTIAL 



KUTURE I)EVEL<>P>IENTS 




doubled, provided the ineohauicul efficiency remained 
constant. 

Unfortunately, transducers with very high me¬ 
chanical Q'h cannot respond fully to very short pul.ses. 
Consecpiently, the requirement that the transmitting 
pulses must be short in order that the water can ab¬ 
sorb the i)ower without cavitating and that the me¬ 
chanical of a magnetostrictive transducer must be 
high to make it capal)le of producing high acoustic 
power levels are inconsistent. It ai)pears, therefore, 
that transducers intended for use at extremely high 
power levels for very short pul.ses should l)e made of 


piezoelectric crystals which have higher electro¬ 
mechanical coupling coefficients than magnetostric¬ 
tive materials and which can be operated at lower 
Q's. This does not mean that magnetostrictive trans¬ 
ducers cannot be used for moderately high ])ower 
applications. For example, the Sangamo 26-kc (^II 
cylindrical tran.sducer, which has an active face ap¬ 
proximately 18 in. in diameter and 16 in. high and 
a mechanical Q of 12, should be capable of giving, 
during short i)ulses, as much as 15 kw of acoustic 
power in the water from about 60 to SO kw of 
electric input i)ower. 


CONFIDENTIAL 



Chapter 13 

THEORY AND DESIGN OF MAGNETOSTRICTION SCANNING SONAR 

TRANSDUCERS 


13.1 FUNDAMENTAL REQl IREMENTS 

13.1.1 Principle of Operation of 
Beam Scanning Systems 

In a typical horizontal .scanning sonar .system the 
transducer is used as a transmitter and as a receiver. 
First, it is used to transmit a strong pulse of high- 
frequency sound into the water uniformly in all di¬ 
rections in the horizontal j)lane. Second, it is used to 
receive the echoes of the original pulse which are 
reflected from \'arious objects in the surrounding 
water in such a manner that the electric receiving 
network connected to the transducer can indicate the 
direction from which the echoes come. The distance 
to the reflecting object is determined from the veloc¬ 
ity of sound in water and the time interval between 
the initial pulse and the reception of the echo. 

Accurate determination of the direction from 
which the echo comes requires that the electric re¬ 
ceiving network, with the aid of the transducer, 
form a sharp directional acoustic receiving beam of 
.sensitivity in the horizontal plane, and this beam of 
sen.sitivity must be rotated in the horizontal plane at 
such a rate that the revolution of scanning requires 
less time than the length of the initial pulse of sound. 
The general scheme is illustrated in Figure 1. 

The beam of receiving sensitivity may be fixed 
with respect to the transducer and the transducer 
rotated, or the transducer may be fixed and the beam 
of receiving sen.siti\'ity rotated electrically with re¬ 
spect to the transducer. This latter system has 
proved to be the more practical because higher scan¬ 
ning speeds can be attained and fewer mechanical 
complications are involved. In general, two types of 
electric rotation of the beam of receiving sen.sitivity 
have been develojied. One of these types involves the 
use of a mechanically rotated commutator which 
links the transducer elements to the beam-forming 
network by electric or magnetic coupling. In the 
other general type the coupling between the trans¬ 


ducer elements and the electric receiving network is 
made through electronic vacuum tubes or their 
equivalent. The electronically rotated .systems can 
use much .shorter pulse lengths than those that are 
mechanically rotated. This gives some advantage in 
signal-to-reverberation ratio, especially if the re¬ 
flecting object is small.“ 



Figure 1. Diagram illustrating the basic principles of 
operation of a scanning sonar system. 


13.1.2 Acoustic Patterns 

Receiving Patterns 

The function of the typical horizontal scanning 
sonar transducer recpiires that it must be made up of 
quite uniform elements arranged .symmetrically 
about a vertical axis. There is evidence to indicate 
that .satisfactory receiving patterns can be produced 
only if the distance between centers of the elements, 
measured around the circumference, does not exceed 
one-half wave length by more than a few per cent. If 
the spacing is greater than this, it appears that the 


CONFIDENTIAL 


36.3 









THEORY AND DESIGN OF MAGNETOSTRICTION SCANNINi; SONAR TRANSDUCERS 


:»66 


height of tlie minor lol)es, 90 degrees or more around 
from the major lobe of the receiving beam, will be too 
great for satisfactory operation. 

A diagram of a simplified rotatable beam-forming 
system for a cylindrical transducer is shown in Fig¬ 
ure 2. A front of a sound wave which advances in the 
direction of the acoustic axis is represented by ww. 
The transducer elements are represented by the coils 
arranged around the periphery of the circle. The.se 



Figure 2. Diagram of a simplified rotatable beam- 
forming system for a cylindrical transducer. 


coils are placed in the geometrical positions occupied 
by the active faces of the transducer elements on the 
actual transducer in the water. Two wires come from 
each transducer element to the commutator device. 
One wire from each transducer element is attached 
to its respective condenser plate on the stator of the 
conden.ser-coupled commutator and the other wire is 
connected to the system ground. Corresiionding to 
each stator plate is a rotor plate which is connected 
through an attenuator re.sistor and a time-delay 
.section to the common output line. 

If the center of the beam-forming network is 
turned in the direction of the acoustic axis, the signal 
output should be maximum. This condition will be 
realized if the time-delay sections introduce as much 
time delay in the signals from the elements as is 
nece.s.sary to compensate for the time delay of the 
acoustic signal in the water. For e.xample, to make 
the signal from element IR come into the output line 
in pha.se with that from element 6R, the lag .section 
in series with element IR shoidd delay the signal l)y 
the .same amount as the water delays the acoustic 
.signal to element 6R, viz., /h .sec. 

If the rotor of the commutator is turned .so that the 
center of the beam-forming network is not on the 
acoustic axis, the signals from the various elements 
are not delayed by the projjer amounts to come into 


the output line in pha.se, and hence the total output 
signal is weak. If the output signal is recorded as the 
rotor of the commutator is turned, a pattern is ob¬ 
tained which is .similar to that obtained by rotating 
a Hat-faced transducer. 

The heights of the side lobes of the pattern may be 
reduced considerably by tapering the amplitude of 
the .signals from the various elements. This is accom¬ 
plished by u.se of the attenuator pads marked A„ in 
Figure 2. The amplitude of the centermost element 
is not dimini.shed, while that of the outermost ele¬ 
ment is dimini.shed to about one-fourth of its normal 
value. A tyj^ical receiving pattern taken with a beam¬ 
forming .system of this general type is shown in Fig¬ 
ure 3. The sj\stem shown in Figure 2 is diagrammatic 
only. In the design of the .system, arrangements must 
be made for tran.smitting as well as for receiving. To 
make the system efficient, care mu.st be taken to 
match impedances properly. 



Figure 3. .\ tyjiical receiving pattern taken with a 

beam-forming system and a 48-element cylindrical 
transducer. 


In the beam-forming network the signal ampli¬ 
tudes aiul jihase .shifts must be held to clo.se toler¬ 
ances if sharp symmetrical acoustic patterns are to 
be obtained. There are several ways in which un¬ 
wanted pha.se shifts can arise in the signals from the 
elements, some of them in the tran.sducer itself, 
others in the beam-forming network. The former are 
of importance in transducer tlesign and construction 
and will be considered here. 

First, the active faces of the tran.sducer elements 


CONFIDENTIAL 




































FUNDAMENTAL REQUIREMENTS 


:i67 


must he accurately aligned around a true circular 
cylindrical surface. Otherw ise the times at which the 
signals in the water arrive at the transducer faces 
will differ from tho.se for which the beam-forming 
network is designed. 

Second, if the elements are rather sharply resonant 
and their frequencies of resonance vary, there will be 
a varying phase difference between the .sound pres¬ 
sure on the active face and the v'elocity of vibration 
of the stack. The phase of the .signal voltage gener¬ 
ated in the windings of a magnetostrictive transducer 
element depends on the jiliase of the velocity of the 
element, and consecpiently any variation of pha.se 
between the driving .sound pressure and the velocity 
of vibration of the element will also result in a vari¬ 
ation in the phase of the generated .signal in the wind¬ 
ing. This mechanical phase variation in radians is re¬ 
lated to the sharpne.ss of mechanical resonance Q 
and the fractional deviation of the frequency from 
the frequency of resonance 5///r by the relation 



where Q = frfih ~ /i), and /2 — fi is the difference in 
the frecpiencies of the half-pow'er points. In degrees, 

(la) 

It is de.sirat)le to keep the phase variation due to the 
variation in the frequencies of resonance of the ele¬ 
ments to within ±6 degrees. This means that the 
fractional variations of the frequencies of resonance 
of the elements used in making a transducer .should 
.satisfy the relation 


A third source of phase variation is that of electric 
impedance of the elements. U.sually the windings of 
the transducer element are electrically terminated 
in appro.ximately their complex conjugate impedance 
at the frequency of re.sonance. Under the.se circum¬ 
stances the current that Hows in the circuit is very 
nearly in phase with the generated voltage in the 
transducer windings. However, assuming that all 
termination impedances are identical, the terminal 
voltages vary with the magnitudes and pha.se angles 
of the impedances of the tran.sducer elements. For 
this rea.son it is important that magnitudes and phase 
angles of the impedances of all the elements in a 
tran.sducer be kept within rather close tolerances. 


Experience has indicated that a scanning .sonar 
tran.sducer gives satisfactory uniformity of patterns 
for all azimuthal directions if the magnitude of the 
impedance of each element is within +5 per cent of 
the average of all of them and the impedance jjha.se 
angles are within ± 2}/2 degrees of the average. 

Figure 4 shows the distribution of the impedances 
of the elements at two different frequencies, one at 
resonance and the other off resonance, for a .satis¬ 
factory 48-element .scanning transducer measured 
in water. 



Figure 4. Graph showing the distriiiution of imped¬ 
ances at two different frequencies of a satisfactory 
48-element scanning sonar transducer, measured in 
water. 



If high-quality receiving patternsarej;.04)eol)tained, 
all elements must make uniforw^acoustic contact 
with the water and be of uniform sensitivity. Ex¬ 
perience with scanning sonar systems has .shown that 
uniform patterns of good quality are obtained if the 
sensitivities of the elements are uniform within 
± 1 db at any given frequency. 

TR.XNSMITTINIf PATTERNS 

The transmitting pattern in the horizontal plane 
should be uniform within ± 1 db. Average perform¬ 
ance may be obtained even if the variation is + 2 db. 
If the elements are sufficiently uniform and well 
matched to meet the receiving pattern requirements 
stated above, they will automatically .satisfy the re- 


COXFIDENTIAL 



































THEORY AM) I)ESH;\ OF MAGNETOSTRICTION Sf:ANNIN(; SONAR TRANSDUCERS 


:{ 6 « 



Figure 5. A tyiiical transmitting pattern in the hori¬ 
zontal plane using a 48-element cylindrical transducer, 
circuit as shown. 


ciuirements for good transmitting patterns. A typical 
transmitting pattern is shown in Figure 5. 

The transmitting pattern in tlie vertical plane 
should he such as to throw as much of the acoustic 
{lower as {possible into the main lobe in the region of 
the horizontal i)lane. Side lobes should be kej)! at a 
minimum but are not critical. The usual |)atterns 
jiroduced by a uniform-line source, in which the side 
lobes are about 13 db lower than the main lobe, are 
generally .satisfactory. If the elements are made u]) 
of .sections s|)aced vertically, with inactive gaps be¬ 
tween the active sections, the height of the .side lobes 
will be greater than —13 db relative to the main lobe. 
An e.xample of this tyiie of vertical {lattern is shown 
in Figure 6. If it is desired to reduce materially the 
heights of the side lobes, it is neces.sary to divide the 
elements into vertical .sections ai3{3roximately 1 wave 
length long, with very short gaps between sections, 
and taper the amplitude from the center in a para¬ 
bolic or gau.ssian manner. It is debatable whether the 
slight improvement in {lerformance that would re¬ 
sult from this adjustment of the vertical {xittern is 
worth the extra trouble and ex{3ense involved in 
effecting it. 



Figure 6. \ typical vertical transmitting pattern of a 
48-element cjdindrical transducer in which the elements 
are made ui) of four vertical sections separated bj" short 
inactive s[)aces. 

One disadvantage of a .shar]) vertical {Dattern is 
that the sound beam overshoots the target submarine 
if the dei)th angle of the submarine as seen from the 
attacking ship exceeds a few degrees. If it is desirable 
to maintain contact with a deep target at closer 
ranges with the horizontal scanning system, it is 
neces.sary either to widen the beam or tilt it down¬ 
ward. However, any broadening of the beam re.sults 
in a lower signal-to-noi.se ratio. In actual {iractice a 
comirromise must be made between the.se factors. 

One proposed solution is to run three wires to each 
of the tran.sducer elements so that the full length of 
the elements can be energized to give a shai’i) vertical 
pattern for general long-range searching, or a fraction 
of the total length of each element can be energized 
to gi\'e a broader vertical beam for maintaining con¬ 
tact with the target at shorter ranges. 

Another way of maintaining contact at shoid 
ranges would be to tilt the sound beam slightly 
downward by mechanically tilting the elements or 
by phasing the vertical .sections of the elements. 
Both these methods, however, are too com|jlicated 
to be practical. 


COXFIDEXTIAL 



















































FUNDAMENTAL REQUIREMENTS 


369 


260 



Figure 7. Relations among active face diameter D frequency /, and number of elements X for cylindrical scanning 
sonar transducei-s. (The distance between the centers of the active faces of the elements is taken as one-half wave length.) 


A more feasible method i.s to supplement the hori¬ 
zontal scanning system with a separate trainable 
depth scanning system or a sharp-beam echo-ranging 
system trainable in three dimensions. In .such “inte¬ 
grated” .systems the horizontal .scanning .system is 
u.sed for general long-range continuous search around 
the horizon, whereas the other system would be used 
to maintain accurate contact with the target at clo.se 
ranges and large depth angles. 

The foregoing comments concerning the vertical 
transmitting patterns apply equally well to the verti¬ 
cal receiving patterns. 

13.1.3 Selection of Frequency 

Attenuation in Medium and Tr.^nsducer Size 

After the pattern requirements are agreed upon, 
the size of the transducer and the frequency of oper¬ 
ation must be adjusted to give those patterns. Usu¬ 
ally the .size of the transducer is limited liy the .size of 


standard .sea chests, domes, and mounting equipment 
on e.xisting ships. The outside diameter of the tran.s- 
ducer i.s usually kept less than 19 in. and the height 
less than 22 or 23 in. The.se dimen.sions automatically 
set a lower limit on the frequencies that can be used 
to obtain the desired patterns. The upper limit is .set 
by the attenuation of the .sound in the water. It is 
well known that the attenuation of sound waves in 
water increa.ses rapidly with increasing frequency. It 
is difficult in practice to get desirable ranges with 
frequencies greater than 60 or 70 kc. With tran.s- 
ducers of the maximum size mentioned above, it i.s 
]io.ssible to get patterns of sati.sfactory sharpness at 
26 to 28 kc. If the transducer is made smaller than 
this, higher frequencies must be used. Figure 7 gives 
the frequencies that should be u.sed for cylindrical 
transducers having different numbers of elements 
and different active face diameters, where the centers 
of the active faces of the elements are separated by 
one-half wave length. 


CONFIDENTIAL 






































.{70 


THEORY AM) DESKiN OF MAf;\ETOSTRICTION SCANNING SONAR TRANSDUCERS 


Response Characteristics and Tolerances 

The type of frequency response de.sired is deter¬ 
mined by two factors. First, it is usually de.sirable to 
have a tran.sducer which is capable of operating effi¬ 
ciently over a band of frequencies so that (1) the 
tuning of the associated electronic circuits is not 
critical; (2) two ships having the same equipment 
and operating as a team can each have their frequen¬ 
cies changed so as not to interfere with one another; 
and (3) any echoes that have con.siderable change in 
frequency due to Doppler shift can be received with 
little loss. Second, the sharpne.ss of mechanical reso¬ 
nance of the transducer elements must be consistent 
with practical manufacturing tolerances of spread in 
resonant frequencies of individual elements in order 
that the requirements on the uniformity of the phases 
of the received signals are met. This requirement has 
already been stated in equation (la). 

In general, it is difficult to make magnetostrictive 
tran.sducers with low Q’s (i.e., broad mechanical 
re.sonance) and high efficiencies. This is due to the 
low electromechanical coupling coefficients of mag¬ 
netostrictive materials and the inherent eddy-current 
and magnetic hystere.sis lo.s,ses in them. The electro¬ 
mechanical coupling coefficient can be increased to a 
limited extent by proper selection and heat treat¬ 
ment of the magnetic materials and by proper design. 
However, up to the present time the upper limit on 
the electromechanical coupling coefficient of mag¬ 
netostrictive materials is about 0.30. Some gain in 
the frequency band width of efficient operation can be 
made by reducing the eddy-current losses to very 
low ^'alues by constructing the transducer elements 
of very thin laminations which are carefully insulated 
from one another. In most magnetostrictive ma¬ 
terials the magnetic hysteresis losses are negligible 
except at very high power levels, where the magnetic 
cycle begins to approach the proportions of the major 
magnetic hysteresis loop. 

In the practical design of a scanning sonar trans¬ 
ducer of the magnetostrictive type the Q is usually 
kept as low as possible con.sistent with the require¬ 
ments on efficiency. 

1.3. 1.1 Efficiency and Power 
Re(|uireinents 

Any echo-ranging .system will perform as long as 
the signal-to-noise ratio is great enough. If the ship 
on which the echo-ranging system is mounted is per¬ 


fectly quiet, the noise against which the signal com¬ 
petes is due to acoustic reverberation and electric 
noise in the system. Unle.ss the efficiency of the trans¬ 
ducer is very low (a fraction of 1 per cent), or the 
de.sign of the electric receiving gear is poor, the noise 
lev'el is due almost entirely to reverberation. Thus, 
under the.se conditions, the signal-to-noLse ratio is 
determined almost entirely by the acoustic pattern, 
and the efficiency of the transducer is of little con.se- 
quence. 

However, if the ship must operate at high speed, 
so that the noise level due to its motion is high, the 
noise level against which the echoes must be di.s- 
tinguished is no longer set by reverberation, but by 
ship’s noi.se. In this case greater ranges may be ob¬ 
tained by use of greater .signal inten.sities up to the 
levels at which the reverberation becomes of the 
order of magnitude of the ship’s noi.se. Under these 
conditions a transducer of high efficiency is de.sirable. 
This is even more true for scanning systems than for 
sharp beam .systems of the QC’ type, because far more 
acoustic power is required to produce the .same .sound 
pressure over the full horizon than is reciuired for the 
sharp beam. The transmitting system should be 
capable of putting at least 1 kw of acoustic power 
into the water. To produce such a great amount of 
sound power, a powerful driving circuit must be u.sed 
and the transducer must be capable of transforming 
it without much departure from linearity due to mag¬ 
netic saturation of the magnetostrictive material and 
without large losses due to magnetic hysteresis and 
eddy currents. Higher efficiency of the transducer as 
a transmitter also gives it greater sensitivity as a 
receiver. 


13.1..5 Mechanical Requirements 

Ruggedness Ag.unst Mechanical Dam.uie 

A complete scanning sonar transducer .should be 
as rugged as possible mechanically, consistent with 
the requirements on its acoustical performance. 
When mounted on the bottom of a surface .ship or the 
topside of a submarine, the transducer is vulneralile 
to .■severe imimcts due to dragging liottom or striking 
wreckage, floating objects, ropes, cables. Such trans¬ 
ducers are also subject to damage by underwater ex¬ 
plosions. The accepted jiractice is to design the trans¬ 
ducers to withstand maximum impulsive pressures of 
500 to 1,000 lb per sc; in. for submarine u.-^e and 300 
to 500 lb per sq in. for surface ship use. 


CONFIDENTIAL 



GENERAL DESIGN 


Corrosion Resistance 

All the externally exposed parts of the transducers 
should be made of corrosion-resistant materials. The 
metals used should not only lie corrosion resistant 
themselves but should not give undesirable galvanic 
battery action when in electric contact with other 
metals exposed to the same sea water. E.xposed 
soldered joints, for e.xample, are never trustworthy. 

Stainless-steel castings have been found to lie quite 
satisfactory in most respects. Navy bronze castings 
have sufficient strength and corrosion resistance, but 
it is difficult to get them sufficiently free from 
porosity to be watertight. 

The exposed rubber parts, which are usually used 
ns acou.stically transparent faces, should withstand 
the corrosive action of grease, oil, and sea water. For 
transducers mounted on the topsides of submarines, 
where they are exposed to sunlight and air, the rub¬ 
ber parts should be highly resistant to decomposition 
and oxidation by light, heat, air, and .salt water. 

W.^TER Tightness 

It is obvious that a transducer should be water¬ 
tight. However, it is not easy to make transducers 
that are watertight and that remain so under service 
conditions. Great care must be taken to see that there 
are no porous spots in the metal parts and that the 
gaskets and packing glands are properly designed, 
constructed, and assembled. The number of water¬ 
tight joints should be kept to an absolute minimum. 
Design details will be considered in a later section. 

13.2 GE.NERAL DESIGN 

13.2.1 Transducer Supports 

Types of ^Iounting 

QC Flange. The standard QC flange is the most 
commonly used transducer mounting and has proved 
to be quite satisfactory in actual service in hundreds 
of installations. Changes to scanning sonar gear from 
standard (^C gear can be made more quickly and eco¬ 
nomically if the scanning sonar transducer is made 
to fit the existing mountings. Figure 8 gives the essen¬ 
tial details of a standard QC flange. The gasket 
groove is in the flange and the tongue that engages 
it is on the transducer. The inside surfaces of the 
tongue and groove are made to fit within a few thou¬ 
sandths of an inch, whereas the outside surfaces do 
not meet by several hundredths of an inch (as shown 
in the A detail in Figure 8) to permit the excess rub¬ 


371 


ber of the gasket to flow out of the groove when the 
transducer flange and the QC' flange are pulled up to 
face-to-face contact by the 12 ^: 4 -in. bolts. The face- 
to-face contact of the flanges is necessary to give the 
full mechanical strength and rigidity of the joint. 
Otherwi.se any bending moment on the joint would 
compress the gasket on one side and relieve it on the 
other, perhaps enough to allow leakage of water. 



Figure 8. Essential details of a QC flange. 

Deck Mounting. For mounting scanning sonar 
transducers on the topside of submarines, the trans¬ 
ducers are usually equipped with a large flange ex¬ 
tending beyond the periphery of the main body of the 
transducer at the base. This flange is bolted to the 
deck. An example of this type of mounting flange is 
shown in Figure 9, an illustration of the HP-3S tran.s- 
ducer arranged for topside deck mounting on a sub¬ 
marine. 

Horizontal Mounts. In depth .scanning sonar sys¬ 
tems, which .scan in the vertical plane, the axis of 
.symmetry of the transducer must lie in the hori¬ 
zontal plane, and the tran.sducer assembly must be 
trainable about the vertical axis. In such transducers 


CONFIDENTIAL 




































372 THEOin AM) I)ESI(;N OK MA(;NET0STRICTION SCAXNINC; SONAR TRANSDUCERS 


Figure 10. .K 20-kc HP-3DS traii.^ducer for depth scan- 
iiiiiK sonar. Gooseneck supiiort attached to a standard 
<dC flange. 

(luccr. By use of a special adaiiter it could also be 
mounted directly on a standard C^C’ Hanse. 

iNlAiN Traxsdi'cer Frame 

General Shape and Strength. The cont'entional 
scanning; sonar transducer is cylindrical in shape, 
with the active faces of the elements on the face of 
the cylinder. The main frames of such transducers 
are generally s])ool-shaped. The side section of a 
typical unit is shown in Figure 12. There are so many 
ways in which elements of various kinds can be 
mounted on the spool that a comprehensive discus¬ 
sion of the subject cannot be given here. In some in¬ 
stances the elements are fI'ee-flooded with water. 
This necessitates covering the windings and lead 
wires with good watertight insulation and providing 
water seals where the lead wires enter the terminal 
box through the flange of the spool. 


the active elements are jilaced only on the two front 
cpiadrants and the lower back cpiadrant. This leaves 
the upper back cpiadrant free for mounting purposes 
if desired. Figure 10 shows a transducer that is sup¬ 
ported by means of a goo.seneck extending from the 
upper back cpiadrant of the transducer to a standard 
QC flange mounting. This type of mounting is diffi¬ 
cult to manufacture unle.ss special machining tools 
are set up. Also, it is difficult to make a satisfactory 
water seal between the case of the tran.sducer and the 
ends of the rubber “blanket” in the vicinity of the 
goo.seneck. (The rubber blanket extends around the 
cylindrical face of the tran.sducer, covering the active 
faces of the elements and making acoustic contact 
between the elements and the water.) 

Another method for mounting depth .scanning 
transducers is illustrated in Figure 11. Here the en¬ 
tire cylindrical surface is co\-ered with a stretched 
rubber boot and the transducer is supported by two 
hollow struts, one from each end bell. Each .strut is 
also used as a watertight cableway. The flanges on 
the tops of the struts make watertight junctions with 
the flanges on the sujiporting casting. This tran.s¬ 
ducer was originally designed to lie mounted on the 
bottom of a .standard horizontal .scanning tran.s- 


Figure 9. 2()-kc I1P-.3.S transducer for topside 

inountiiiK on a submarine. 


CONFIDENTIAL 








GENERAL DESKJN 


37:1 



Figure 11. 38-kc HP-8 transducer for depth scan¬ 

ning sonar with two-strut support. 


In other cases the space around the elements is 
vacuum-filled with castor oil or its equivalent. When 
this method is used, the space for the elements, and 
therefore the rubber-boot joints and the seals where 
the lead wires enter the terminal box, must be 
vacuum-tight. The portion of the lead wires that 
pas.ses through the seals must be made of solid wire, 
since stranded wire will not form a vacuum-tight 
seal. 

In those cases where the ti-ansducer elements are 
surrounded by air, no vacuum seals are required for 
the lead wires. This is the simplest, and preferred, 
construction. 

Except where the elements are free-flooded with 
water, the pre.ssure of the water outside the tran.s- 
ducer produces a crushing effect on the tran.sducer 
frame. In designs similar to that shown in Figure 12, 
the total hydrostatic force exerted on the bottom 
plate is brought to bear on the outside edge of the 
bottom flange. The shear strength of the bottom 
flange must be made great enough to withstand this 
force (irR~p). The force on the top flange is nearly as 
great but is more evenly distributed. The core of the 
spool must bear the longitudinal compression result¬ 
ing from the force on the two ends of the transducer 
and the circumferential compression due to the in¬ 
ward radial force transmitted by the transducer ele¬ 
ments from the water. If the outside radius of the 



Figure 12. Side section of siiool frame for transducer 
for horizontal scanning. 


transducer is Ro, the mean radius of the spool core i?i, 
the wall thickness of the spool core t, and the outside 
water pressure p, then the longitudinal compressive 
stress in the spool core is 


and the circumferential compressive stress is 

^2 

Sc = yp- (4) 

If the allowable compressive strength of the metal 
from which the spool core is made is of the order of 
35,000 lb per sq in., the wall thickness .should be 
about 0.30 in. to withstand a maximum water pres¬ 
sure of 1,000 lb per .sq in. 

Materials. The spoollike frame of the tran.sducer 
must be watertight, strong, and corrosion-resistant. 
Ordinary boilerplate steel is nonporous and strong, 
but will corrode .severely in .sea water. However, ex¬ 
perimental scanning sonar tran.sducer frames have 
been made of pieces cut from boilerplate sheets 


CONFIDENTIAL 




























































S71 


TiiKORV AND df:sk;n of magnetostriction scanning sonar transducers 


welded together. The finished assembly was usually 
cadmium-plated or painted with red navy j^aint. 
Such construction ju-actice is not recommended for 
permanent installations because corrosion would 
eventually cause trouble. 

Navy bronze (Navy M-4()-B-8) castings are me¬ 
chanically strong and highly resistant to corrosion, 
but unless the casting is tlone under ideal conditions 
considerable trouble is caused by water leakage due 
to porosity in the metal. For experimental purposes, 
jjorous castings can be made watertight by carefully 
tinning them with solder or by vacuum-impregnat¬ 
ing them with special thermosetting resins, but the 
practice is not recommended for permanent installa¬ 
tions because corrosion may open ui? new leaks at 
anj" time. It is jmssible that centrifugal casting would 
eliminate {jorosity in navy bronze castings. 

Stainless-steel castings, made by the Allegheny 
Ludlum Steel Corporation, have ])roved the most 
.satisfactory for transducer frames up to the present 
time. This material is strong, corrosion-resistant, and 
comparatively free from poro-sity. It is somewhat 
difficult to machine with ortlinary tools because of its 
tendency to harden by the action of the heat gener¬ 
ated lyy the cutting tool. However, if hard sharp 
cutting tools are used, the machining jjresents no 
great difficulties. 

13.2.2 Design of Active Face Area 

F.\ce Area Required 

It has been pointed out in Section 13.1.4 that a 
horizontal scanning sonar transducer should be capa¬ 
ble of putting roughly 1 kw of sound jiower into the 
water. When the jieak sound pressure in water 
reaches atmospheric jiressure (about 10 '^ dynes 
per SCI acoustic power per sq in. is about 

2.2 watts. If it is assumed that the maximum possible 
.sound pre.ssure is limited to this value by cavitation, 
the active face area of the transducer would have to 
be about 450 sq in. to give a total .sound power of 
1 kw. On this same basis, a transducer having an 
active face 173^ in. in diameter and 14 in. high should 
1)6 capable of emitting 1.7 kw of .sound i)ower from 
its 770 SCI in. of active face area without danger of 
cavitation. If the same transducer were 10 ft below 
the surface of the water, the additional pressure 
would permit it to radiate 3 kw of sound jiower with¬ 
out danger of cavitation. 

It has been shown by Ma.son and others at the Bell 
Telephone Laboratories that, for short pidses, radi¬ 


ation intensities consideralily greater than 2 watts 
per scj in. can be produced in water at atmospheric 
])ressure, and that the maximum sound pre.s.sure at¬ 
tainable without cavitation occurring increase's with 
decrea.sing pul.se length. Although it has not as yet 
been fully demonstrated, it is possible that a 1734 X 
14-in. scanning .sonar transducer in 10 ft of water 
could radiate as much as 5 kw of sound power into 
the water during 0.035-.sec pulses without trouble 
from cavitation. If this is the case, then it .should be 
jiossible to radiate 1 kw of sound power into the 
water with a transducer having about 200 s(} in. of 
actual face area. This would accordingly be the [irob- 
able lower limit of the active surface area which a 
conventional .scanning sonar transducer should have. 

Length and Width of Elements 

The length of the active faces of the elements of a 
scanning sonar transducer is determined by the de¬ 
sired vertical iiattern. To give a pattern of the type 
shown in Figure 0 , in which the main lolie is about 
12 degrees wide at —10 dl), the length of the ele¬ 
ments should be about 7 wave lengths. The effect on 
the pattern of altering the velocity amplitude of vi¬ 
bration along the length of the elements has been 
di.scus.sed in Section 13.1.2. There it is shown that 
inacti\'e spaces between segments along the length of 
an element should be kept to a minimum in order to 
keep down the heights of the minor lobes. 

Figure 13 illustrates .several po.s.sible designs of the 
active face area of the elements of .scanning .sonar 
transducers. Table 1 gives the corresponding total 
active face areas for a tran.sducer mea.suring 1734 X 
1 () in. and the ratios of the active areas to the total 
a\'ailable area for the seven different designs shown 
in Figui-e 13. The element marked 1 is made up of a 
series of acti\ e circular' areas such as would be pro¬ 
duced by consti'ucting the element of a .series of tube- 
and-plate oscillator units in which the plates would 
be in the shape of cii'cular buttons. Such a design 
would pi'oviile .sufficient active face ai-ea and could be 
I'eadily adapted to give side-lobe i-eduction by ampli¬ 
tude shading. The element mai'ked 5 is essentially 
the .same as 1 . 

The element marked 2 in Figui’e 13 is made up of 
four- segments .separated by inactive gaps which ai’e 
about ’4 wave length long. This design was u.sed in 
the Harvai'd HP-3 and the Sangamo HP-5 trans¬ 
ducer's in which each element is made uii of four 
laminated stacks. The inactive space between seg¬ 
ments is rerprir'ed for the windings, and caps, and 


CONFIDENTIAL 



GENERAL DESIGN 


375 


supporting structure. The design provides sufficient face lias been pointed out in Section 13.1.2. It is 
active face area and gives vertical patterns of the equally important to have the center lines of the 
form shown in Figure (5. A rough foi-m of amplitude active face areas spaced at ecpial angles around the 
shading can be attained with this type of element by circumference of the cylinder. This prevents the un¬ 
adjusting the amplitude of each stack. equal time lags that would otherwise occur in the 

arrival of the sound waves at the centers of the ele- 
r.\BLE 1. Total .\ctive Face .Areas and .Area Katio.s ments for different azimuthal positions of the acous- 
for Different Designs of .Active Faces, as Shown in 

Figure 13. _ 


Element 

Ratio of 
active area 
to available 

area 

-Area for 
17I4X 10 in. 
transducer 
(sq in.) 

Radiation 

eff 

Quality of 
vertical 
pattern 

1 

0.81 

710 

Good 

Good 

2 

0.88 

770 

Good 

Good 

3 

0..j0—0.80 

440—700 

Poor to fair 

Poor to fair 

4 

1.00 

880 

Gooil 

Good 

5 

0.80—0.90 

700—790 

Good 

Good 

f) 

0..30—0..)0 

260—440 

Poor 

Good 

7 

0.30 -1)..50 

260—440 

Pool' 

Good 


The element marked 3 is an extreme example of the 
2 type and is not recommended because of poor radi¬ 
ation efficiency and un.satisfactory vertical pattern. 

The element marked 4 makes u.se of all the avail¬ 
able face area and is probably superior to the other 
designs shown. The design can be realized by use of 
a single long laminated stack for each element, or by 
a long stavelike metal diaphragm with magneto- 
stiictive tubes or stacks to drive it. The Harvard 
HP-f and HP-2 scanning sonar transducers have 
this type of active face area. 

The design for elements (i and 7 calls for quite nai- 
row active face areas, which woukl be obtained if the 
elements were radially jilaced laminated stacks with 
the planes of the laminations parallel to the axis of 
the trairsducer. Such types have been ])roposed and 
have been experimented with in the f(jrm of small 
models. Active face areas of this design should gi\’e 
satisfactory vertical and horizontal patterns in trans¬ 
mitting and receiving. The chief fault of the de.sign 
is that it does not make efficient use of the available 
radiating ai'ea. Moreover, the radiation efficiency is 
low l)ecause each active face area is bounded by wide 
pres.sure-release areas, causing the sharpness of me¬ 
chanical resonance to increase (higher Q) and reduc¬ 
ing the maximum amount of acoustic power which 
can be radiated. 

Accuracy of Location of Elements 

The importance of placing the active faces of the 
elements accurately on a circularly cylindrical sur- 



SHADED AREAS REPRESENT ACTIVE 
FACE AREAS 

Figure 13. Diagram illu.stratiug several po.s.sible de¬ 
signs of active face area. 

tic axis relative to the transducer (see Figure 2). At 
26 kc, for example, each U.f-in. error in position of 
the center of the element causes a phase error of 
about 16 degrees. 

The supports of the elements should be designed so 
that the elements are held accurately in position in 
spite of the normal impacts and jostling that a trans¬ 
ducer receives in ordinary service. The effects of 
pressure waves due to near underwater explosions 
should also be taken into account in the design of the 
supports of the elements. 


CONFIDENTIAL 



































376 


THEORY AM) DESIGN OF MAGNETOSTRICTION SCANNING SONAR TRANSDUCERS 


13.2.3 Overall Shape and Mount¬ 
ing of Elements 

Space Available for Elements 

The space available for each element of a scanning 
■sonar transducer is somewhat limited. It has already 
lieen pointed out that the distance between the cen¬ 
ters of the active faces of the elements should not 
e.xceed one-half wave length (in water) by more than 
a few per cent. Measured in inches, this distance is 
about 28.5//, where / is in kc. If the elements are 
of the longitudinal vilirator type, the length of the 
elementary oscillators in their direction of vibration 



Figure 14. General .shaiie and size in inches of space 
available for elements in a typical 48-element trans¬ 
ducer designed to operate at / kilocycles. 


will be between one-fourth and one-half of a wave 
length in the magnetostrictive material used. If 
nickel or .some similar material is used for making the 
o.scillators, the distance in inches the elements e.xtend 
radially inward from the active face is between 
47.5// and 95//, where / is in kc. 

The general shape and dimensions (in inches) of 
the space available for single elements in typical 
48-element transducers are shown in Figure 14. The 
entire element, comjilete with its supporting and 
housing structures, must lie within this space. The 


limited space for each element and the desirability of 
ha\'ing as large an active face area as possilde make 
it difficult to design element .structures that are sup¬ 
ported and watersealed independently of each other. 
Many attempts have been made in this direction 
without any notable succe.ss. However, .se\'eral of the 
general designs of element .supjiorts and housings 
that have been used or proposed are shown in follow¬ 
ing illustrations. 

HP-2B Type 

Figure 15 shows a design in which the elements 
consisted of single long stacks of nickel laminations 
con.solidated with re.sin and ecjuiiiped with end caps 


SPACE INSIDE RUBBER 
BOOT vacuum-filled 



Figure 1.5. General design of element support and 
hou.sing used on Harvard HP-IB and HP-2B scanning 
sonar transducers. 


held to the ends of the stacks l\v cement and by a tie 
rod extending through the stack from one end to the 
other. The elements were held to the flanges of the 
supporting spool by screws which engaged the end 
caps. In one version of this design the elements were 
exposed directly to the water, .so that the windings 
had to be of the watertight insulated type. In an im¬ 
proved form of ilesign, the whole assemlily of ele¬ 
ments was surrounded by a watertight pc rubber boot 
and the space between the boot and the elements 
filled with castor oil or its equivalent to gi\'e acoustic 
contact l^etween the elements and the water. The 
spaces between and in back of the elements and be¬ 
tween the windings and the laminated stacks were 
filled with a good pressure-release material, such as 
coriirene or air-cell neoprene, to prevent excessi\-e 


COXFIDEXTIAL 






























GENERAL I)ESK;N 


377 


mechanical daminng and undesirable acoustic cou¬ 
pling of the vibrating elements. 

HP-3 Type 

Figure Ki shows a general ilesign in which the en¬ 
tire transducer is housed in a watertight, sound- 
transparent rubber boot with air-filled space around 

■^c rubber foce strip 
Cjrcie-^eided to faces of 



Figure 16. General design of element support and 
housing used on the Harvard HP-3 scanning sonar 
transducer. 


the elements. The elements do not have separate 
housings. In this case acoustic contact is made be¬ 
tween the active faces of the laminated stacks and 
the water through a thin rubber face strip, which is 
CVcle-Welded to the face of the laminated stack, 
through a thin film of castor oil, and then through 
the rubber boot. The boot was made approximately 
12 per cent under size so that it had to lie stretched 
to fit over the transducer. The tension developed in 
the stretched boot produced intimate acoustic con¬ 
tact with the castor-oil film on the smooth rubber 
face strijis on the elements. These face strips were 
of rubber, molded to the proper radius of curvature 
on the exposed face. The inward radial pressure 
exerted by the stretched rubber boot is given by the 
expression 


where t is the wall thickness of the boot, E the 
Young’s modulus of the rubber, R the mean radius 
of the boot when stretched, and AR/Ro is the frac¬ 
tional increase in radius of the boot due to the 
stretching. A boot ^ in. thick, with a mean final 
diameter of 18 in. and a Young’s modulus of 300 lb 
jier sq in., will give an inward radial pres.sure of about 
2 lb per sq in. when stretched 12 per cent. 

The stretching of the circumference of'the rubber 
boot causes the boot to shorten in the axial direction, 
because of the Poisson ratio effect. This must be al¬ 
lowed for in specifying the length of the unstretched 



PERCENT INCREASE IN LENGTH 

Figure 17. Graph showing fractional change in width 
of a pc ruhher strip which is due to stretching it longi¬ 
tudinally by various fractional amounts. 

boot. Figure 17 shows the relationship between the 
fractional change in width of pc rubber as a function 
of the fraction change in length due to stretching. 

There are many ways of .supporting the individual 
laminated stacks in this type of general design. In the 
Harvard HP-3 tran.sducer, four laminated stacks are 
fastened together end to end liy a common rubber 
strip on the face and an aluminum spline on the back 
to form the long stavelike elements that are fastened 
to the flanges of the supporting spool at each end. In 
the Sangamo HP-5 transducer, each of the 48 ele¬ 
ments is composed of four laminated stacks, mounted 
one above the other. Each stack is supported at both 
ends by means of flat, ring-shaped support disks 
which lie between the end caps of the four circular 
layers of stacks. Each layer comprises 48 stacks, one 
for each element. The molded bakelite end caps of 
the stacks have two jirotruding bos.ses, which engage 
holes in the support disks and hold the stacks ac¬ 
curately in position. In this type of construction the 
wires connecting the four stacks of an element can¬ 
not be permanently connected until all the stacks in 


CONFIDENTIAL 


































378 


THEORY AND i)ESh;n OK Ma<;netostri(:tion scanning; sonar transducers 


the transducer are in place. C'onversely, it would be 
very difficult to replace an element without disas¬ 
sembly of the entire transducer. But in spite of the 
difficulty in repairing or servicing it, this type of 
mounting is still among the best available because of 
its mechanical accuracy, strength, and reliability. 



Figure 18. General de.sign of element supi)ort and 
housing using stacks of IIP-3 - like laminations ce¬ 
mented to resin-imiiregnated glass fiber face strips. 

HP-3 WITH Plastic Face Strip 

Figure 18 shows a similar design, in which the me¬ 
chanical support of the laminated stack elements is 
provided l\v the strong, relatively thick face strips, 
which extend along the full length of the element and 
fasten to the flanges of the suiiporting spool at each 
end. These face strips can be made of any material 
that has the reciuisite strength, low density, and small 
acoustic damping and can be bonded secure!}' to the 
faces of the laminated stacks. All the metals, with the 
po.ssible exception of magnesium, are so dense as to 
increase the mass reactance of the \'ibrating system, 
and thereby the mechanical Q, by an undesirable 
amount. No complete transducer of this type has ever 
been constructed, but preliminary exjieriments indi¬ 
cate that the best materials for the face strips are 
certain of the resin-impregnateil glass fiber laminates. 
These materials have all the desirable mechanical 
characteristics listed above. 

The shape of the laminated stacks used with this 


type of const I’uction is not limited to the form shown 
in Figure 18. In fact, it would be entirely possible to 
replace the laminated stacks with tube-and-plate 
type units, for example, scpiare magnesium blocks 
bearing nickel tubes and coils. 

If the type of construction illustrated in Figure 18 
were to be used, the simjilest element would be made 
by a uniform stack extending the full length of the 
element without gaps or amplitude shading. If de¬ 
sired, amplitude shatling could be secured by insert¬ 
ing narrow inactive gaps in the stack at selected in¬ 
tervals, in accordance with some amplitude shading 
cuiA'e. It is also po.ssible to make the element in many 
segments, each with a sejiarate winding of the proper 
number of turns to give the desired amplitude shad¬ 
ing. In this ca.se no special end cajis would lie re- 
(luired for the segments so that the inactive spaces 
between them would need to be only wide enough to 
accommodate the windings at the ends of segments. 

One important advantage of this type of construc¬ 
tion is that the elements are strong separate mechan¬ 
ical units which can be jiut in or taken out of the 
transducer with very little trouble. 



Figure 19. General design of element support and 
housing in the Harvard I IP-2 scanning sonar trans¬ 
ducer. 


HP-2 Type Transducer AIounted in C’ontainers 
Figure 19 shows the general design of the element 
support and housing used in the Harvard HP-2 scan¬ 
ning sonar transducer. This was the first major at- 
temiit at housing the elements in separate watertight 
containers. These were made of approximately 


CONFIDENTIAL 































GENERAL DESIGN 


379 


0.032 in. thick stainless-steel sheet formed into ta¬ 
pered cans and were lined with air-cell neoj^rene to 
provide pressure-release .support for the laminated 
stacks on all sides except the active face. The molded 
rubber faces were Cycle-Welded to the active face of 
the stack and to the inside surface of the containers 
in a single operation. 

RUBBER FACE STRIP CYCLE- 
WELDED TO LAMINATED STACKS 
AND BONDED TO STAINLESS - 



water seals into the terminal box. A detailed desci'ip- 
tion of this transducer will be found in Chapter 14. 

The chief advantage of this type of construction is 
that the elements are mechanically, electrically, and 
acoustically independent of each other. Removal and 
replacement of elements are relatively easy. Further¬ 
more, the elements have consideralile mechanical 
strength except at the edges of the containers. There 
are disa(h’antages, however. These include the large 
number of water seals that must remain peidectly 
tight under all service conditions, the vulnerahilit}^ 
of the edges of the containers to damage by impacts 
from external objects, and the difficulty of getting 
the acti\’e faces of the elements arranged accurately 
at equal angles and on a true circle. In the one HP-2 
transducer that was constructed, small leaks de¬ 
veloped in the C'ycle-Welded joints between the 
rubber faces and the stainless-steel cans. After much 
exi)ei'imentation, this tran.sducer was modified to the 
form shown in Figui-e 15. 


BOILER PLATE STEEL DIAPHRAGM 



Figure 21. General design of element support and 
housing used on the Harvard “millerphone” scanning 
sonar transducer. 


Figure 20. General design of element support and 
housing as proposed in the Harvard SP-1 scanning sonar 
transducer. 

The two lead wires from the windings on the lam¬ 
inated stack were brought through a small stainless- 
steel tube at one end of the container. A watertight 
seal was made between the solid lead wires and the 
stainles.s-steel tube by filling it with Rubberseal com¬ 
pound. When the complete elements were mounted 
in the suiTporting spool the little tubes through which 
the lead wires passed projected through holes with 


SP-1 Type Transducer Mounted in Containers 
Figure 20 shows another form of self-contained 
water-tight element construction, designated as the 
Harvard SP-1 type. C’onstruction of this type was 
abandoned, however, because of the difficulties ex- 
lierienced with the leakage of the C.vde-Weld joints 
in the Harvard HP-2 transducer and because experi¬ 
ments on a small model showed that the narrow 
width of the active face did not have enough radi¬ 
ation resistance to give a sufficiently low Q. There 
were two definite advantages to this t 3 q)e of con- 



CONFIDENTIAL 



















































THEORY AM) DESIGN OF MAGNETOSTRICTION SCANMNi; SONAR TRANSDUCERS 





Figure 22. General design and element support and 
housing for a tube-and-plate type of scanning sonar 
transducer. 


WATERTIGHT MOLDED CORPRENE STEEL BAR 



Figure 23. General design of element support and 
housing for a tube-and-plate type of scanning sonar 
transducer with rubber boot. 


struction, however: (1) the independent housing of 
the elements and (2) the natural adaptability to 
\-ertical amplitude shading for the reduction of minor 
lobe heights in the vertical acoustic pattern. 


BRONZE QUARTER-WAVE ELEMENT 
DIAPHRAGMS FASTENED TO SUP¬ 
PORTING SPOOL FLANGES AT 



housing for a permanent-magnet, polarized nickel 
scroll type of scanning sonar transducer. 

BRONZE CASTING MACHINED ON 



Figure. 25 General design of elements and housing for 
a scanning sonar transducer with special impedance 
matching wedges integral with the diaphragm. 


“[NIillerphone” Tube-and-Plate Type 
Figure 21 shows a design of the tul)e-and-plate 
type of transducer adapted to the general form re¬ 
quired for scanning sonar use. In this type the dia¬ 
phragms of all the elements were an integral part of 
a cylindrical steel .shell which had deep longitudinal 
notches on the inside or outside surface to reduce the 
mechanical coupling from one element to the ne.xt. 


CONFIDENTIAL 








































































GENERAL DESIGN 


.181 


Ihe cylindrical steel shell served as the watertight 
hoii.sing for the transducer, the diaphragm for the 
elements, and the mechanical support for the interior 
structure. The toj) and bottom caps of the transducer 
made a tongue-and-groove water seal with the top 
and bottom edges of the cylindrical shell. This trans¬ 
ducer was much lighter than the laminated stack 
type. 



Figi're 26. General de-^sign of the elements and housing 
of a .scanning sonar transducer using a laminated resin- 
impregnated fiber-gla.ss cylinder for the outside water¬ 
proof housing and element support. 

One transducer of this sort was constructed at 
HUSL. Tests showed its efficiency to be low but 
satisfactory. However, the frequency-matching of the 
elements was so unsatisfactory that the transducer 
was given up as a failure on this score as well as on 
account of its inherent mechanical weakne.ss. 

Tube-axd-Plate with Individual Sealed Dia- 

PHRAG-M.s 

The various designs described in the foregoing 
paragrajihs have all been e.xecuted as experimental 
models for the scanning sonar program at HUSL. 
In the search for magnetostrictive transducers that 
would meet the requirements, a number of ideas were 
proposed, some of which were discarded without e.x- 
perimental study. Figures 22 to 26 are presented 
partly to trace the cour.se of the laboratory’s efforts 
and partly with the thought that they may be of 
as.sistance in future development. Prominent in these 
suggestions are (1) the de.sirability of a design that 
will allow the removal of single elements and (2) an 


attempt to adapt to .scanning sonar u.se the tran.s- 
ducers already successful in other applications. The 
structural features of the various designs are indi¬ 
cated in the figures. The merits and defects of the 
\-arious designs are briefly summarized as follows. 


Fig. Type 


Merits Objections 


22 


23 


24 


2.5 


26 


Tube-and-plate 


Tul)e-and-plate 


Quarter-wave 
bronze wedge 
driven by hairpin 
laminations 


Bronze wedges 
cast integrally 
with shell, driven 
by book-type 
laminations 


Plastic cylindrical 
shell, driving ele¬ 
ments cemented to 
inner surfaces 


(a) Permits verti¬ 
cal shading 

(b) Separate ele¬ 
ments remova¬ 
ble 

(a) Permits verti¬ 
cal shading 

(b) Separate ele¬ 
ments remova¬ 
ble 

(c) Mechanically 
strong 

(d) Small number 
of water seals 

Separate elements 

removable 


Xo supporting 
spool needed 


Plastic shell pro¬ 
vides water seal, 
support for ele¬ 
ments, and acous¬ 
tic window 


(a) Large number 
of water seals 

(b) Structurally 
weak 


(a) Too sharply 
resonant 

(b) Possible inter¬ 
element me¬ 
chanical 
coupling 


(a) Too sharply 
resonant 

(b) Poor a-c mag¬ 
netic flux cir¬ 
cuit 

(c) Structurally 
weak 

(a) Too sharply 
resonant 

(b) Structurally 
weak 

(c) Requires d-c 
polarization 

(a) Elements not 
removable 

(b) Can be assem¬ 
bled only as a 
cornidete unit 

(c) Structurally 
weak 


Ladderphone 

Figure 27 .shows the design of a transducer known 
as the Harvard ring ladderphone, [H-RLP], This 
transducer will be considered here only for the design 
of its housing and support. The elements consist of 
adjacent jiairs of legs, effectively fastened together at 
inside and outside ends by continuous face arches. 
This arrangement introduces mechanical and mag¬ 
netic coujiling between neighboring elements, which 
affects the phases and amplitudes of the signals gen¬ 
erated in the windings of the elements when the 
transducer is excited by plane waves. Thus the re¬ 
ceiving beam-forming network which must be used 
with this type of transducer may be slightly different 
from those used with tran.sducers which have me¬ 
chanically separated elements. 


CONFIDENTIAL 






















382 


THEORY AND DESIGN OF MAGNETOSTRICTION SCANNING SONAR TRANSDUCERS 


The laminated ring-shaped stack is supported on 
corprene pads between the top and bottom flanges 
of the spool. The laminated stack alone has sufficient 
mechanical strength to withstand most of the abuses 
anticipated by the regular specifications. The water¬ 
tight housing is provided by a pc rubber boot which 
is Cycle-Welded to the outside surface of the lam¬ 
inated ring stack and clamped at its ends again.st the 
edges of the flanges of the supporting spool. 

/Oc RUBBER BOOT 
CYCLE-WELDED TO OUTSIDE 
SURFACE OF LAMINATED 



Figure 27. General design of the elements and housing 
for the Harvard 36-kc “ring ladderphone” scanning 
sonar transducer. 


Tubular-Type Elements 

There are many po.ssible ways in which tubidar- 
type transducer elements can be used to make up 
scanning sonar transducers. Figure 28 shows a design 
in which an array of tubular elements of the B-19H 
monitor type is mounted around the periphery of a 
supporting spool. One of several possible ways in 
which tubular transducers may be mounted on a 
supporting spool and the lead wires brought into the 
terminal box is suggested in the partial side-section 
drawing shown in Figure 28. It will be seen that the 
lead wires are brought out through a metal tube in the 
top cap of the transducer element tube and the small 
metal tube is passed through a water seal into the 
terminal box. In this type of construction, however, 
the entire transducer would become flooded if one 
element leaked. Some method of water-sealing the 
lead wires in the stem tube would eliminate this 
effect. 

It would also be possible in construction of this 
type to use laminated ring-stack elements or tubular 


units made up as laminated scrolls. At the time of 
writing it is unfortunately not iTossible to make radi¬ 
ally vibrating thin-walled tubular transducer units 
which give efficiencies greater than a few per cent. 
Thicker-walled stacks of rings can be made to luiT'e 
high efficiencies in the frecpiency region of their me¬ 
chanical resonance, but because of the ratio of the 
velocity of sound in magnetostrictive materials com¬ 
pared to that in water the wave length of the sound 
in water at the frecpiency of resonance is nearly equal 



Figure 28. General design and mounting of the element 
type of scanning sonar transducer. 


to the diameter of the ring stack. Thus, to maintain 
the required one-half wave-length spacing between 
elements, the ring stacks would have to be operated 
at one-half their freciuency of resonance where their 
efficiency is not much greater than that of thin- 
walled tubes or scrolls. The resonant frequency of 
ring stacks may be reduced by increasing the ma.ss 
loading and decreasing the stiffne.ss by such methods 
as cutting notches in the periphery of the rings and 
bonding heavy copper windings to the stack. Such 
methods result in the transducer having a higher me¬ 
chanical Q at a lower frequency, but the higher (J 
makes it necessary to operate close to the frequency 
of resonance and makes it more difficult to keep the 
elements within the necessary close phase tolerances. 

Figure 29 shows the design of an early tubular-type 
scanning sonar transducer in which the elements con¬ 
sisted of arches of magnetostrictive material placed 
around the periphery of the supporting spool. The 
considerable extent of soldered joints made it fairly 
susceptible to corrosion and leakage. This fact, to¬ 
gether with the requirement of d-c polarizing current 
and very low efficiency, led to its abandonment. 


CONFIDENTIAL 


























GENERAL DESIGN 


38;{ 


annealed corrugated 

NICKEL STAMPINGS SDL- 



Figure 29. General design of elements using the 
multiple arch system. 


rounded by a large rubber boot, with the space be¬ 
tween the boot and tubes filled with castor oil or its 
equivalent, the elements would still be liable to 
damage by imjtact. 

The inherently low efficiency of tubular trans¬ 
ducers makes it impractical to use them for trans¬ 
mitting the powerful sound pulse reciuired in normal 
scanning sonar operation. This would necessitate the 
use of some more efficient transducer as a sound 
source, with the tubular scanning sonar transducer 
used as a receiver only. 

General 

In the preceding sections a number of general de- 



Figure 30. Typical design of the terminal box on a scanning sonar transducer with free-flooding elements and windings. 


An outstanding weakness of alt scanning sonar 
transducers made of tubular elements is their liability 
to mechanical damage from impacts of sharp objects 
against the sides of the transducer. Tubes of the type 
required will readily withstand 500 lb per sq in. hy¬ 
drostatic jTressure but are easily crushed by heavy, 
sharp objects. Even if the array of tubes were stir- 


signs for scanning sonar transducer elements, mount¬ 
ings, and housing have been suggested and discussed 
briefly. There are many other basic forms and end¬ 
less combinations of the basic forms. Several have 
been tried experimentally but at the time of this 
writing only two of the types have proved practical, 
viz., those .shown in Figures 15 and 10. 


CONFIDENTIAL 












































































38i 


THEORY AND DESIGN OF MAGNETOSTRICTION SCANNING SONAR TRANSDUCERS 


ONE of FOUR CABLES 

-TERMINAL BOX 

CABLE SEAL/ CAP PLATE 


M’TG flange to MATCH 
QC FLANGE 



RUBBER FACE 
on ELEMENT 


ELEMENT HOUSED 
in STAINLESS-STEEL 
CAN 


WINDINGS 


Figure 31. A terminal box de.sign for a scanning sonar transducer with separately housed watertight elements. 


13.2. i Terminal Box and Cable 
Seals 

1. Mo.st scanning sonar tran.sducers are ecjuipped 
with cables before installation on ships. These cables 
are shipped separately, however, and must occasion¬ 
ally be changed because of damage or wear. There¬ 
fore, it is not feasible to attach the cable wires di¬ 
rectly to the lead wires from the transducer elements. 
Instead the lead wires from the elements and the 
conductor wires of the cable are terminated on lugs 
on a terminal board in the transducer. 

The terminal board is located in that j)art of the 
transducer commonly called the terminal box or 
terminal chamber, which is usually located at one 
end of the supporting spool to make it as accessible 
as possible. Present practice is to place the terminal 


box on the end of the transducer which is opposite 
the end attached to the support. This permits acce.ss 
to the terminal box by merely removing the cover 
plate and eliminates the need to disconnect the 
transducer from its supiiort. A typical arrangement 
is shown in Figure 12. 

The terminal box should be both watertight and 
vaportight. This latter reciuirement means that the 
cable must enter tlie terminal box through a seal or 
jjacking gland. If this precaution is not taken, water 
\’apor diffuses down the hollow center of the training 
shaft and condenses on the cold walls of the sul)- 
merged transducer. In addition to sealing against 
water and vapor, it is good practice to install a 
packet of dehydrated silica gel to absorb any small 
amounts of water or water vapor present in the 
terminal box at the time it is closed. 


CONFIDENTIAL 



























































































GENERAL DESIGN 


385 



Figure 32. A terminal box design for a scanning sonar transducer in which the terminal board lug.s are replaced by 
4 A-N plug.s. The elements are housed in a common castor-oil-filled chamber surrounded by a rubber boot. 


A second rea.son for sealing the caltle entry to the 
terminal box is to prevent water from flowing up the 
training shaft into the ship in case of damage to the 
watertight covering of the tran.sducer. 

2. If the transducer elements are free-flooding, or 
if the elements are in separate watertight housings, 
the element lead wires must enter the terminal box 
through water seals. Solid (not stranded) lead wires 
and solid watertight insulation must be used if leak¬ 
age from the insulation or the housing of any one 
element is not to interfere with the ojjeration of the 
other elements. Stranded wire conductors or unim¬ 


pregnated textile insulation under the insulation 
sheath will permit seepage of water through the 
water seal if the water enters the wire at any place 
along its length. 

Figures 30 and 31 .show two typical de.signs of 
terminal boxes for tran.sducers with free-flooding or 
.separately housed elements. In Figure 30 the ele¬ 
ments consisting of laminated stacks of nickel wound 
with waterproof insulated wire are immersed directly 
in the sea water. The lead wires from the elements 
are passed through water seals into the terminal box 
and .soldered to the lugs on the terminal board. The 


CONFIDENTIAL 
































































































386 


TIIKOKV AND DESIGN OF MAGNETOSTRICTION SCANNING SONAR TRANSDUCERS 


cable is brought through a large seal in the top of the 
terminal box and the wires from it are connected to 
the i)roper lugs on the terminal boaixL The terminal 
box is finally sealed by the bottom caj) plate. 

Figure 31 shows a terminal box design forascanning 
sonar transducer with separately housed watertight 
elements. Here the terminal box is at the top end of 
the transducer for convenience in mounting the ele¬ 
ments on the spool. Each element is housed in a stain¬ 
less-steel can, from which a stainle.ss-steel tube pro¬ 
jects. This tube passes through a water seal into the 
terminal box. The solid wires from the windings pass 
through the tube into the terminal box. The.se are 
water-.sealed in the tube with Rubberseal compound 
confined between two plugs of bakelite as shown in 
the diagram. The.se seals are to prevent flooding of 
the terminal box and of the remaining elements in 
case one element should leak. This type of seal is very 
effective and reliable, although it is difficult to .serv¬ 
ice. In this particular model the total cable was made 
up of four separate watertight cables, each of which 
])assed through a water seal in the top cap plate. The 
individual wires of the cable were soldered, as usual, 
to the proper lugs on the terminal l)oard. 

A modification of this terminal Ixaxrd design which 
makes it po.ssible to remove the cable and toj) cap 
plate from the transducer with comparatively little 
troul)le is shown in Figure 32. In this modified design 
the lugs on the terminal board are replaced by four 
A-N plugs. The female parts of the plugs are fastened 
to the bakelite terminal board and the male parts to 
the cable wires. The cable can be removed from the 
transducer by loosening the water .seals in the toj) cap 
jxlate of the terminal box, unfastening the toj) cap 
plate and sliding it U]3 along the cables, then disen¬ 
gaging the A-N plugs. The cable is reconnected to 
the transducer by following the reverse procedure. 
It is often veiy convenient to have the cable easily 
removable from the tran.sducer and it is especially 
so when a tran.sducer must be installed through a 
hole in the side of a sea chest which is too small for 
the transducer with its cable attached. 

3. The design of the terminal bo.xes for scanning 
sonar transducers in which the elements are enclosed 
in a single castor-oil-filled chamber .surrounded by a 
rubber boot is not very different from the design for 
those with free-flooding elements. For the oil-filled 
transducer, the seals must be vacuum-tight as well as 
watertight, whereas lead wires and windings do not 
require heavy watertight insulation becau.se castor 
oil (or its equivalent) is a good insulating material. 


A design with the terminal box at the toj) end of 
the transducer is shown in Figure 32. The seals where 
the lead wires pass from the oil-filled chamber to the 
terminal box are made l)y pa.s.sing the two solid, 
enamel-covered lead wires through holes in specially 
molded rubber gasket pieces. The pressure exerted by 
the plunger of the seal squeezes the rubber against 
the outside wall of the seal and against the solid 
wires, making a complete vacuum-tight seal. 

The terminal board and cable seal arrangements 
for this design have already been discussed in Sec¬ 
tion 13.2.4. 

Figure 33 shows a design with the terminal box at 
the bottom of a tran.sducer in which the elements are 
immersed in castor oil. In this ca.se the individual 
wires are brought through seixarate seals consisting 
of solid rods threaded at each end, insulated from the 
metal frame by bakelite bushings, and sealed by 
rubber gaskets which are scpieezed between the 
bushings. 

The cable seal shown for this case is the pothead 
type in which the wires of the cable i)a.ss through 
holes in a bakelite disk at the ba.se of the pothead and 
the wires are sealed by pouring in Rubbenseal com- 
l)ound, a thermosetting resin, or similar material. 
The cable above the pothead is sealed against water 
or vapor by a sheath made of firehose or its equiva¬ 
lent. The pothead itself is sealed to the baffle plate 
in the transducer spool. 

4. When the elements are mounted in an air-filled 
space, no seals are needed where the lead wires from 
the elements enter the terminal box. In a transducer 
of this type, a water leak in the element chamber 
w(Kdd flood all the elements, making the entire tran.s¬ 
ducer inoperative, so that there would be little pur¬ 
pose in having the terminal box remain dry. An ex¬ 
ample of this type is shown in Figure 12. Here, the 
wires pass through holes in the flange of the spool to 
the lugs on the terminal board. 

5. The location of the cable seal in the tran.sducer 
is determined chiefly by its accessibility. It should be 
placed at some point between the terminal box and 
the flange which supports the transducer so that, if 
there should be any leakage in any part of the sup- 
jxorting shaft or its flange, the water cannot enter the 
terminal box. In conventional horizontal scanning 
transducers it has been the practice to locate the 
cable seal within the spool core near the top or the 
bottom end. Typical cases are illustrated in Fig¬ 
ures 12, 30, 31, 32, and .33. 

In transducers designed for scanning in the vertical 


C(4NFIDENTIAL 



GENERAL DESIGN 


387 



Figure 33. A design for a terminal box located in the bottom of a scanning sonar transtlucer in which the elements are 
immersed in castor oil. 


plane, the elements are usually divided into left and 
right halves to give hearing deviation indication 
[BDI].*'' Each half has its own terminal board. In 
some designs the double cable recpiired was brought 
through a single cable seal, as in the first form of the 
Harvard HP-3DS tran.sducer (see Figure 10). A 
cable seal of the type shown in Figui-e 33 was used 
at the position of the flange on the transducer, as in¬ 
dicated in Figure 34. This cable and water seal were 
later replaced by two SO-twisted-jmir telephone 
cables and two packing-gland seals located at the 
same position as the pothead seal. The packing-gland 


type of cable seal is preferred, provided satisfactory 
watertight sheathed cable is available. 

Another arrangement for the cable seals and ter¬ 
minal box for depth scanning sonar transducers is 
shown in Figure 35. Here a cable passes through each 
of the two supporting flanges and the cable seal is 
located in a “dutchman,” which is inserted between 
the transducer flanges and the supporting flanges. 

(j. It is desirable to have the cable or cables .sealed 
on the outside of the sheath and between the indi¬ 
vidual conductor wires at the place where they leave 
the terminal box. Such double sealing not only pre- 


CONFIDENTIAL 































































































388 


THEORY AND DESIGN OF MAGNETOSTRICTION SCANNING SONAR TRANSDUIIERS 


FIRE HOSE SHEATH 
CLAMPING BANDS 
CABLE MADE OF TWISTED PAIRS 
POTHEAD 

RUBBERSEAL COMPOUND OR RESIN 

MATCH TO QC FLANGE 


GOOSENECK 



RUBBER BLANKET SUR¬ 
ROUNDED BY TIGHT .010 
NICKEL BANDS 


ELEMENTS - 


ONE OF TWO TERMINAL- 

BOARDS SPOOL CORE- 

Figure 34. Terminal box and cable seal design used in the HP-3DS depth scanning sonar transducer. 


vents the entrance of water or water vai^or into the 
terminal box through the inside of the supporting 
shaft, but also prevents the leakage of vapor or water 
between the individual wires of the cable. The sealing 
of the individual wires is desirable but not essential 
because the rate of flow of water or vapor between 
the wires of a compact multiconductor cable 40 or 
50 ft in length is very small. 

The terminal box cable seals illustrated in Fig¬ 
ures 12, 30, 31, 32, and 35 are of the conventional 
packing-gland type in which a rubber gasket is 


squeezed tightly against the outside of the cable 
sheath and the inside packing-gland wall. In seals of 
this type, the gasket should grip a length of the cable 
at least as great as half the diameter of the cable and 
preferably as great as the diameter. Likewise, the 
bushings, or parts of the seal on each side of the 
gasket, shovdd extend a distance approximately 
equal to the diameter of the cable. 

If the length of cable against which the gasket 
squeezes is too small, the seal may gradually loosen 
because of the cold-flow of the sheath material, with 


CONFIDENTIAL 














































































GENERAL DESKLN 


.{89 



a con.secjnent “liourglas.s” tleformation. This effect 
can be minimized Ijy ii.se of close-fitting l)iishings, 
which give the cable .sheath good .support on each 
side of the pres.sure gasket. 

Some of the characteristics of cable seal designs of 
the packing-gland type are shown in Figure 3(5. 
Part A shows a .seal that is pooi- becau.se the gasket is 
too thin and because the cable sheath is not given 
proper .support on each side of the gasket. The pre.s- 
sure of the thin gasket causes cold-flow of the sheath 


material away from the gasket i-egion and a bulge out 
beyond each narrow gasket washer. The .seal shown 
in part B has adequate width and thickness but the 
washers or bushings are not long enough to give the 
cable sheath sufficient support to minimize cold- 
flow. The seal .shown in part C is very good, provided 
the bushings fit the cable sheath clo.se enough to 
minimize cold-flow of the sheath material. The di¬ 
ameter clearance of the bushings from the cable 
should b(‘ approximately 2 per cent of the diameter 


CONFIDENTIAL 














































































































390 


IHEORY AND DESKiN OF MACiNETOSIKIClTION SCANNINC; SONAR TRANSDUCERS 


of the cable. Part D shows a seal that may he tight¬ 
ened from each end. Part E shows a seal that is de- 
signetl to seal and hold a cable against the very high 
water in-essures encountered by submarines which 
go deep and are subjected to jiressure waves set up by 
depth charges. Under very high pressures a cable is 
likely to slide through a packing gland, much like a 
piston rod. In such cases it is good practice to mokl 



^ POOR. PINCHES OFF 
CABLE ond LOOSENS 
WITH AGE. 



FAIR. BUT CABLE SHEATH 
SHOULD HAVE BETTER SUPPORT 
AT EACH END OF GASKET. 



CABLE SHEATH. 



6000 IF BUSHINGS FIT PROPERLY. 



E DOUBLE SEAL USED FOR HIGH-PRESSURE 


SUBMARINE INSTALLATIONS. 

Figure 36. Some de.signs of cable seals of the packing- 
gland type. 

one of the gaskets directly to the sheath of the cable. 
There are many possible t'ariations in the design of 
packing-gland seals, but whatever they are they 
should use gaskets of adeciuate radial and longi¬ 
tudinal thickness and should give the calile sheath 
side sujTport for a sufficient distance on each side of 
the gasket. 

To jtrevent leakage of water through the spaces be¬ 
tween the many conductors of a sheathed cable 
which is sealed on the outside by a conventional 
jiacking-gland type of seal, it is necessary to fill all 
the spaces between the conductors with a lilocking 
material such as tar or resin. One jiopular method is 


to introduce a monomer lipuid into the interstices of 
the calile conductors in the region of the seal and 
cause this liiiuid to polymerize to form a gummy-to- 
hard resin. When the cable must be flexilile on each 
side of the seal, care should be taken that the resin¬ 
forming liijuid is not allowed to penetrate too far on 
either side of the seal. 

The pot head type of cable seal illustrated in Fig¬ 
ures 33 and 34 is most often used with homemade 
cables made up of twisted jiairs of single wires. These 
jiothead seals are made by threading each wire 
through its proper hole in the base plate of the pot. 
Then the space between wires in the ]iot is filled with 
material such as Rubberseal compound (or some 
thermosetting resin), which adheres closely to the 
wires and to the sides of the pot. Seals of this type 
haT-e proved satisfactorily watertight. Their me¬ 
chanical strength to withstand hydrostatic pressure 
is determined by the strength of the pot and its bot¬ 
tom plate. The examples shown in Figures 33 and 34 
were not designed foi- high mechanical strength. 

13. 2 . .5 Cables for Scanning Sonar 
Transducers 

1. In most scanning sonar systems the scanning 
commutator is located inside the ship. It is necessary, 
therefore, to run wires from each element of the 
transducer to the commutator chassis, u.sually 40 to 
50 ft away. To minimize electromagnetic and electric 
]iickup and cross talk in these long wires, it is good 
jiractice to use a twisted pair of confluctors from each 
element. Because of pickup and cross-talk troubles 
it is not good practice to connect one terminal of 
each element to a common ground in the transducer 
or to a common shield of the cable. It has been found 
jireferable to bring out both wires from each element 
to the commutator chassis. When three or more leads 
are brought from each transducer element, these 
shoidd be run in the cable as a twisted midtiplet. 
When the lead wires are run in the cable as twisted 
pairs or multijilets, there is no need for a common 
electric shield around the whole cable. The conduc¬ 
tors forming the cable should be color-coded to elim¬ 
inate the necessity of “ ringing through” and marking 
each wire with a label. 

The bundle of wires forming the cable should be 
surrounded by a watertight sheath. The comjilete 
cable should be as flexible as possible, especially when 
the transducer must be trained to point in different 
directions with resiiect to the ship by rotation of the 


CONFIDENTIAL 




































































GENERAL DESIGN 


391 


transducer shaft. In such cases a stiff cable would be 
worn out in a few weeks of steady operation, due to 
internal straining and rubbing of the conductors in 
the cable. In this respect, solid wire conductors are 
particularly un,satisfactory because they “work- 
harden” and break when subjected to continuous 
Hexing and twisting. The insulation on the individual 
conductors should be capable of withstanding abra¬ 
sion against neighboring conductors. Abrasion can be 
minimized by use of certain waxy lubricants. If the 
cable is to be properly flexible it shoukl have a core 
of some pliable material, such as hemp or jute, and 
the sheath .should not bind the conductors together 
too compactly. 

For those installations in which the transducer 
must be rotated, the cable should be able to with¬ 
stand, during continuous duty, tor.sional rotation of 
3b0 degrees or more in both directions in about 10 ft 
of length. A number of specifications may be laid 
<lown for construction of a .satisfactory cable. (1) The 
resistance of the individual conductors should not be 
greater than 10 ohms per 1,000 ft. (2) The insulation 
i-e.sistance between any pair of wires should be at 
least 10 megohms for 1,000 ft of cable. (3) The elec¬ 
tric capacity between the wires of any twisted pair 
should not exceed ai)proximately 50 mmf per ft and 
the cajiacity between any two wires not in the same 
twisted multiplet .should not exceed about 30 mmf 
l)er ft. (4) The cross talk between any two twisted 
pairs should be less than —50 db. (5) The strength 
of insulation between any two wires in the cable 
should be at least 1,000 volts. ((5) The insulating 
material should have reasonably low dielectric hys¬ 
teresis loss in the frequency region of 10 to 00 kc. 

The outside diameter of the cable should not ex¬ 
ceed 1 Yl ; if.sheath should be watertight, tough, 
and flexible and resistant to al)rasion and to deteri¬ 
oration by action of grea.se, oil, .salt water, air or sun¬ 
light. It should have as little tendency as possible to 
cold-flow when under pres.sure from the gasket of a 
cable seal. Several of the .synthetic aiul natural rub¬ 
ber compounds meet most of these requirements. 
In some scanning sonar transducer cables, rubber- 
lined fire hose has been used satisfactorily as the cable 
sheath. 

The cable should be able to withstand and operate 
at temperatures up to aboin 170 F and down to 
about 20 F. Cables with Vinylite insulation on the 
conductors or Vinylite sheaths become soft anrl weak 
at the higher temperatures and stiff at the lower, 
possibly causing some impaii'ment in iDerformance. 


Neoprene or rubber insulations, on the other hand, 
seem to be satisfactory in this respect. C'ables in¬ 
tended for use on submarine installations should 
be able to withstand external pressures of at least 
1,000 lb per sci in. without damage to the internal 
in.sulations or the sheath. 

2. The cables used on the earliest scanning sonar 
transducers were constructed at HUSL Ijecause com¬ 
mercial cables with the j^roper characteristics were 
not immediately available. 

Details of construction of the one that proved 
reasonably satisfactory for a 48-element .scanning 
sonar transducer are given in Chapter 14. This had 
the general appearance and flexibility of a manila 
rope. Provided with a loose-fitting fire hose and sealed 
into the terminal box with a pothead seal of the type 
shown in Figures 33 and 34, this cable met the re- 
((uirements outlined above in an experimental in¬ 
stallation on board .ship. 

A Navy-approved armored telephone cable, 
TTHFA-50, meets most of the specifications, but it 
is too stiff for installations in which the transducer 
has to be rotated. At present there is no commercial 
cable that is .satisfactory for scanning sonar in all 
regards, and a develojiinent program looking to the 
production of such a cable is highly desirable. 

13.2.6 Acoustic Contact Between 
Elements and the Water 

The problem of getting good acoustic contact be¬ 
tween the vibrating elements and the water is an im¬ 
portant one, especially so when the elements are 
housed in watertight casings. Included in this prob¬ 
lem is the nature of the .surface that makes contact 
with the water. Some surfaces have a greater tend¬ 
ency than others to collect or generate gas bubbles. 
Even a small collection of these bubbles on the active 
face of a transducer can cause poor acoustic contact 
with the water. A smooth surface exposed to the 
water gives much less trouble than a rough one, and 
for this reason metal surfaces frequently prove 
troublesome unless they are smoothly coated with 
certain paints or enamels. Smooth rubber surfaces, 
free from oil or grease, are usually satisfactory. Bub¬ 
bles are most likely to collect when the transducer is 
j)ut into water that is colder than itself. The warm 
transducer increases the temperature of the water in 
contact with it, causing some of the dissolved gas to 
come out of solution and accumulate on its surface. 

Transducers with free-flooding elements usually 


CONFIDENTIAL 



.{92 


rHEOKY AND DES1<;> OE MACiNETOSTRICTION SCANMNC; SONAR TRANSDICERS 


present few problems in maintenance of acoustic 
contact when j^recautions are taken against the con¬ 
dition just described. With metal-faced transducers, 
smooth, nonjiorous material that is re.sistant to cor¬ 
rosion and electrolysis should be used. Uncoated 
steel is notably poor in these respects. Stainle.ss steel 
and Navy M bronze are usually cjuite .satisfactory. 
Experiment has shown that uniform and rej^roduc- 
il)le acoustic contact between most metals and water 
can be obtained if the metal is coated over with some 
nonporous, water-re.sistant, firmly adhering paint. 
\’inylite, rubber, neoprene, or i^olystyrene base 
paints have been found to be well adapted to this 
purpose. The active faces of laminated stacks are not 
perfectly .smooth even when the stacks are con¬ 
structed with the greatest care and are, therefore, 
apt to collect bubbles on their surfaces when in direct 
contact with the water. One of the best means of ob¬ 
taining good contact between the stack face ami 
water is to cement rubber, or its ecpiivalent, secui-ely 
to the face of the stack. 

The most .satisfactory bond between the laminated 
stacks and rubber faces .so far found at HUSL is 
made with Cycle-Weld 55-() resin. An example of a 
design making use of this type of acoustic contact 
with water is shown in Figure 19. If the laminated 
stack elements of a complete tran.sducer are housed 
by a single rubber boot, acoustic contact may be 
made between the rough active faces of the stacks 
and the inside of the rubber boot by vacuum-filling 
the space between the elements and the boot with a 
licjuid like castor oil or its ecpiivalent. An example of 
this type of construction is illustrated in Figure 15. 

Another method is illustrated in Figures 1(5 and 18. 
Here molded face sti’ips of rubber or other suitable 
material are bonded .securely to the active faces of 
the laminated stacks. The rubl^er boot is made 12 to 
15 per cent undersize so that when it is stretched on 
the transducer it makes tight contact with the face 
strips of the elements. A film of castor oil is painted 
on the faces of the elements and on the inside surface 
of the rubber boot before they are put together. The 
film of castor oil aids the acoustic contact between 
the face strips and the rubber boot lyy filling in small 
irregularities in both .surfaces. The external water 
pressure helps to make this acoustic contact more 
nearly perfect. 

In special cases in which the rubber en\-elope can¬ 
not be made in the form of a complete cylindrical 
boot, the neces.sary pres.sure on the rubber may be 
secured by .sui’rounding the out.side of it with narrow 


thin bands of stainle.ss steel and drawing the.se tight 
by means of turnbuckles (see Figure 10). The thick¬ 
ness of the bands .should not exceed 0.015 in. and the 
width should not be greater than 1 in. The turnbuckle 
assembly rec|uired to tighten the bands is .somewhat 
clumsy, difficult to .streamline, and vulnerable to 
damage by catching on external objects. 

13.2.7 Streamlining of Scanning 
Sonar Transducers 

In any echo-ranging system on shipboard, the 
tran.sducer must be mounted so that no part of the 
ship’s hidl interferes with the reception or transmis¬ 
sion of sound through the water. In surface .ships the 
transducer should be placed well below keel level, 
and for topside submarine mounting the transducer 
should be iilaced in a position where none of the 
superstructure interferes .seriously with the sound 
beam. These reciuirements make it neces.sary to place 
the transducer in the fastest paid of the water stream 
around the ship, and streamlining in some form be¬ 
comes essential. 

The .solution may be to streamline the transducer 
itself as much as possible without interfering with its 
acoustic behavior, but, if it is intended that the 
sound gear operate .sati.sfactorily when the ship’s 
speed exceeds 10 or 12 knots, it is necessary to sur¬ 
round the tran.sducer with a streamlined dome hav¬ 
ing a length-to-width ratio of the order of 3 or 4. At 
water speeds greater than 10 oi- 12 knots, turbidence 
occurs around the .surface of the large cylindrical 
transducer, producing a great amount of acoustic 
noise, which masks the relatively weak echo signals. 

Acoustic considerations limit the amount of 
streamlining that can be applied directly to the main 
body of a scanning sonar transducer. Hence the 
streamlining must be limited to rounding all sharp 
corners and irregularities on the ends and edges of the 
tiansducer body. This is msually accomplished by the 
use of spun .sheet-metal fairings or specially .shaped 
blocks of wateri)roof wood. 

If a transducer is to be u.sed without the jirotection 
of a dome, some consideration should also be given to 
the mechanical effects of the water stream on the 
active face. The mechanical abu.se, by the water, of 
the active face of a tran.sducer mounted on the top- 
sitle of a submarine is cjuite .severe when the sub¬ 
marine is cruising on the .surface at .such a level that 
the waves break over the bow and cra.sh into the 
transducer. The impacts of the waves might cause 


CONFIDENTIAL 




DESIGN OF VIBRATING ELEMENTS 


393 


some flapping of the rubl^er boot against the element 
faces and perhaps some distortion of the elements. 
Figure 9 illustrates one way of holding the rubber 
boot firmly against the element faces and at the same 
time giving mechanical strength and protection to 
the face of the transducer without acoustic inter¬ 
ference. 


13.3 DESIGN OF VIBRATING 

ELEMENTS 


13.3.1 General Considerations 


Retiuirements for the generation of acoustic power 
by a scanning sonar transducer and the limitation 
on the mechanical and electrical ])hase \'ariation 
have been set forth in .sections 13.1.3 and 13.1.4. The 
tolerance on the mechanical phase variations among 
the elements automatically sets the tolerance on the 
product of the Q„ and the 5 ///uvk. Consequently, 
if Qm is large, then 5 ///uvk must be small, and vice 
versa. Since Qm, the maximum efficiency, the cou¬ 
pling coefficient, etc. are all related and are all in¬ 
volved in the design of transducer elements, the rela¬ 
tionship will be discussed at this point. 

Liquation (81) of Chapter 3 gives the relation 


Eff 


max 


—\ 
1 

}^’luQywQc' 


1 - 


Qrn\ 
Qya ) 


in which keti is the effective electromechanical cou¬ 
pling coefficient; Qrn' is the Q shown by the motional 
admittance circle when the measurement is made 
with the transducer loaded by water radiation re¬ 
sistance; Qc (the electrical Q) is the ratio of the reactive 
and conductive components of the clamped-core 
admittance; and Qr.i is the Q shown by the motional 
admittance circle when the transducer is subjected 
to no radiation loading. The first factor of the right- 
hand side of equation (81) of Chapter 3 may be 
thought of as the electromechanical efficiency, that 
is, the fraction of the electric ini:)ut iDOwer that is con- 
\’erted into mechanical power. The second term may 
be thought of as the purely mechanical efficiency 
which is the fraction of the total mechanical power 
radiated as acoustical power. If Rl is the radiation 
resistance and is the equivalent internal frictional 
resistance, then the mechanical efficiency is 


Qya 


Rl 

Rl + RJ 


27r/,iA/* 

RJ 


and 


Qya — Qyw 


Qya 


Qyw 


2wfoM* 
Rl + RJ ’ 


(G) 

(6a) 


where/o is the fretiuency of resonance and M* is the 
equivalent mass of the vibrating parts, i.e., the mass 
which, when vibrating with the same frequencj" and 
amplitude as the active face, has the same kinetic 
energy as the actual \’ibrating system. 

I.,et us now su])i)Ose that a magnetostrictive trans¬ 
ducer element is made which has a gi^Tn geometry, 
magnetic circuit, windings, etc., but that the area of 
the radiating face can be changed without altering 
any of the other characteristics, so that z, can be va¬ 
ried while Ayr f, Qc, and Qva (or/?„,") remain constant. 
It will be of interest to study briefl,y the effect on the 
efficiency due to \mrying Rl- This is important in 
design because the ratio of the radiation resistance 
to the internal frictional resistance should be ad¬ 
justed roughly to give maximum efficienc.y. 

Let Rl = Then, the mechanical efficiency 


Eff,„ 


Rl 

Rl + Rm" " X + l’ 


(7) 


ami the electromechanical efficiency (eciuations (81) 
of C’hapter 3 and (1) and (la) of this chapter). 


Eff„„ 


A’ pffQcQr.i 


A’effQcQlM + 1 + .r 


( 8 ) 


Two cases will be considered. First, a typical tube- 
and-plate type of transducer will be used to illustrate 
the effect of a low Ayff and, second, a typical lami¬ 
nated stack made of thin ring laminations will be 
used to show the effect of a high Ayff. 

1. Typical values for a tube-and-plate transducer 
are: A^ff = 0.0011, Qc = 5.0, Qya = 180. The.se 
values give 


Eff,„, 


0.99 

1.99 + x’ 


Eff total = (Eff,„„)(Eff,J. 

The values of these three efficiencies and Qrw are 
plotted against x in Figure 37. The electromechanical 
efficienc.v drops steadily and the mechanical effi¬ 
ciency increases as the radiation load increases. The 
total efficiency reaches a broad maximum of 16 per 
cent in the I'egion of Rl =1.4 Rm", at which the Qyw 
isabout 75. Forpractical puri^oses it would be better to 
de.sign for /?/. = 4 R„", which would give an efficiency 
of about 12 per cent and a Qyw of 35. The adjustment 
of i?L in a design of this type can be accomplished by 
changing the area of the face associated with each 


CONFIDENTIAL 















391 


THEORY \M> DESIGN OF MAGNETOSTRICTION SCANNINi; SONAR TRANSDUCERS 


tube and chanffinp; the thickness of the plate accord¬ 
ingly to pi’ovide the same mass load for each tube. 

2. Typical \-alues for a stack of thin annealed 
nickel rings are: A^ff = 0.057, Qc = 7.0, Qya = 45. 
The.se values give 


h]ff 


em 


Eff 


total 



—)■ 

1 + x/ 


The values of the three efficiencies and the values of 
Qyw are plotted against x in Figure 38. The rela¬ 
tively large values Avff and Qc keep the electrome- 



Figure 37. Relation between the efficiency and Hl R'm 
for a tyi)ical jdate-and-tube type (WE.\-1), on the a.s- 
snmption that 2irfM* R"„ = Qa is constant and Ri. is 
varied. 


chanical efficiency at a high level even though the 
load re.sistance is increa,sed to large values, fn this 
case the total efficiency reaches a broad ma.ximum 
of 05 per cent at O' = 4, where the Qi ir = 9. Even 
at a Qrn’ = 2, the total efficiency is of the order of 
40 per cent. This performance is about the best that 
can be obtained from magnetostrictive ring stacks 
made for practical use. fn j)ractice the ratio of 
RijR’m for ring stacks can be most easily controlh'd 
by adjusting the ratio of the wall thickness to radius. 

The last example shows the importance of large 
^•alues of A'eff and Qc in keeping the electromechanical 
efficiency at relatively high values. The Avff is de¬ 
termined by the geometry of the magnetostricti\’e 
vibrator, by the perfection of the magnetic circuits 
for the polarizing flux and high-freciuency flux, and 
by the kind of magnetostrictive material which is 
used, its heat treatment and degree of polarization. 
The highest possible value of Avff is obtained from a 
magnetostrictive vibrator in which all the parts of 


the magnetic path in the magneto.stricti\-e mah'rial 
are subjected to a uniform alternating mechanical 
strain and uniform o])timum polarization. This set of 
conditions is realized in a stack of rings or a tube in 
which the direction of the flux and the mechanical 
strain is circumferential and uniform, fn this case 

, ( 47rXVr'V 

■ K^r 

The Avff is less than this for all the vai'ious kinds of 
longitudinal \ ibrators because the mechanical strain 
is not uniformly distributed along the magnetostric¬ 
tive parts of the magnetic circuit, fn .such cases it is 



Figure 38. Relation between the efficiency aiul Ri, Rlh 
for a stack of thin annealed nickel laminations. It is 
a.ssumed that Qya = 2irfM* RH, is constant and that 
Rl is varied. 


all the more im])ortant to do everything possible to 
keep the XV/ factor as large as po.s.sible. p,' is the ef¬ 
fective reversible permeability of the complete mag¬ 
netic circuit. 

Occa.sionally reque.sts are made for magnetostric¬ 
tion transducer elements which are 75 per cent effi¬ 
cient at a Q,„ of about 4. To show how difficult it 
would be to make a tran.sducer element of the longi¬ 
tudinal vibrator type having these characteristics, 
the case will be analyzed. By using gri'at care in the 
coiLstruction of the unit, it might be po,s,sible to make 
the mechanical efficiency as great as 90 per cent. 
C'onseipiently the electromechanical efficiency would 
have to be about 85 per cent. This reiiuires that the 
value of A'pff Q)-n- Qc be about 5.5. The maximum at¬ 
tainable value of A/ff for this type of o.scillator is 
about 0.035. As Qm- is reipiired to be 4, it follows 
that Qc would have to be about 40. This high elec¬ 
trical Qc for the clamped-core impetlance could be 
obtained only by the use of very thin laminations, 
so that the eddy-current losses wovdd be very small. 


CONFfDENTfAL 
















DESKiN OF VIHRATINC; ELEMENTS 


r^ven the use of thin laminations would not be ef¬ 
fective in maintaining the high Qc at high power 
levels on account of magnetic hysteresis losses. \"erv 
thin laminations are difficult to punch and handle. 
A very large number of them are recpiired to give the 
recpiisite stack height. C'on.sequently, in practical 
design and construction work it is generally better 
to use thicker laminations and higher Q,„’s to get 
high efficiencies. 

13..3.2 Tubular Transducer Elements 

Transducers made of relatively thin-walled mag- 
netostrictive tubes (i.e., with wall thickne.ss to diam¬ 
eter ratios of the order of 0.025) which oscillate in 
the radial direction are noted for their flatness of 
frequency response, uniform horizontal patterns, and 
moderately low efficiency. Tran.sducers of this type 
would, therefore, make good elements for a scanning 
sonar transducer intended primarily for listening 
over a wide frequency range. 

A design of this type is illustrated in Figure 28. 
In this design each element would consist of a com¬ 
plete tubular transducer of the B-lQII type described 
in Chapter 5. The length of the tubes should be 
about 4 to 7 wave lengths of the sound in water at 
the frequency used. The outside diameter of the tubes 
should not e.xceed O.G the wave length of sound 
in water at the highest frequency to be used. The 
frequency of resonance in kilocycles of tubes of this 
type is about 00 D, where D is the mean diameter in 
inches but the C is so low that the resonance is not 
very pronounced. The efficiency al.so has a small 
maximum at the frequency of resonance. 

The natural frequency of radial resonance of a 
tubidar type transducer can be lowered by effectively 
decreasing the circumferential stiffness without re¬ 
ducing its ma.ss. It is possible that this result could be 
obtained by corrugating the tube lengthwise so that 
the circumference of the tube is a wavy circle. By ad¬ 
justing the width and depth of the corrugations, al¬ 
most any mass-to-stiffne.ss ratio within reasonable 
limits can be produced, and consecpiently the fre- 
(juency of resonance can be controlled towatxl lower 
values, although the mechanical Q would increase. 
By this method it should be possible to make tubular 
transducers with freciuencies of resonance low enough 
so that the outside diameters of the tubes are less 
than the corresponding wave lengths of sound in 
water. Tubular transducers of this kind coidd be used 
as elements in a scanning sonar transducer of the 


39.i 


type illusti-ated in Figure 28 and could be operated 
at frequencies up to their resonance without difficulty 
from poor patterns. It is (piestionable whether any 
gain in efficiency could be made in this way, as com¬ 
pared to the uniform circular tube, because some of 
the circumferential stiffness of the tube is due to 
bending stiffness, and tleformations caused by bend¬ 
ing give no net magnetostrictive action. This would 
effectively reduce the electi-omechanical coui)ling 
coefficient. 

.\nother variation of the tubular type of scanning 
sonar element is illustrated in Figure 29. This has 
been called the “tubular-arch” type. In this design 
one element consists of an adjacent pair of tubular 
arches which are welded or .soldered down to the 
solid backing plate. It can be shown that the fre- 
(jiiency of resonance in the extensional mode of vi¬ 
bration of such an arch, which is rigidly hinged at 
each end, is the same as that of a complete tube ha^•- 
ing the same radius. Thus if the tul)ular arches are 
semicircular and have a span of % in., the frequency 
of re.sonance (without load) would be about 160 kc. 
The spacing between elements is about in., and 
if this spacing is held below one-half wave length the 
highest freciuency at which the transducer should be 
operated is about 28 kc. Thus the tubular-arch tran.s- 
ducer elements would have to be operated at fre¬ 
quencies far below their re.sonance, with consequent 
loss in efficiency. The efficiency of this type of ele¬ 
ment is not very high at best, because of too great 
water radiation loading, eddy-current losses, and an 
inherent shorted turn. Furthermore, it is almost im¬ 
possible actually to construct the units so that the 
arches are uniformly and firmly attached to the 
backing plate at each edge. Direct-current polarizing 
is recjuired to produce the polarizing flux. 

Another type of radially ^•ibrating tube is the 
laminated stack of rings, wound toroidally. The nat- 
tural frecjuency of vibration of such ring stacks is the 
same as for tubes, i.e., about 00 D kc where D is the 
mean diameter of the rings in inches. Consequently 
the wax'e length of the sound in water at the fre- 
(}uency of re.sonance is about equal to the diameter of 
the tube, which is inconsistent with the requirement 
for .scanning sonar transducers that the elements be 
spaced one-half wave length apart. To satisfy the 
last requirement, the ring stacks would have to be 
operated at approximately one-half their natural 
frequency, with consequent lo.ss in efficiency. How¬ 
ever, if the ring laminations are made thin enough to 
make the eddy-current lo.s.ses very small, and if the; 


CONFIDENTIAL 




.{96 


thf:ory and i)f;sign of magnetostriction scanning sonar transducers 


wall thickness of the ring stack is made sufficiently 
thin to lower the Q to the order of 3 to 5, the stacks 
can still be made t(i ojierate at half-resonance fre- 
(luency with an efficiency of the order of 10 to 15 per 
cent. If the resistive loading of a ring stack or tube is 
due entirely to water radiation resistance, its me¬ 
chanical Q .should be 30.5 t R, where t is the wall 
thic'kness and R the mean radiu.s. Thus to get a Q 
of 5 the t/R ratio should be about 10. 

If the stacks are wound toroidally, the polarizing 
flux has to be circumferential. The polarizing flux 
provided by the remanence flux is sufficient if the 




Figure 39. Suggested iletails of construction of a ring 
stack element for a scanning sonar transducer. 

rings are made of semiannealed nickel or 2^"-Per- 
mendur and if the ring stack elements are not driven 
magnetically beyond 10 or 12 oersteds (peak) during 
transmission of pings. If higher transmitting powers 
are recjuired, the remanence polarization of ring 
stacks must be aided by some d-c polarizing current 
flowing in the windings in the proper direction. 

A .suggestion for making the long slender ring 
stacks into strong self-supporting units that could be 
mounted between the two flanges of a supporting 
si)Ool is shown in Figure 39. The bakelite core is sug¬ 
gested because a shorted turn around the ring stack 
would be produced if the core were made of metal 
that would make electric contact with the metal sup¬ 


porting spool at eac'h end. A metal core would lie 
satisfactory if its ends were insulated from the spool 
flanges. The complete array of ring stack elements 
would be housed within a rubber boot, and the space 
ai'ound the elements would be vacuum-filled with 
castor oil or its eiiuivalent. 

The rings used in making the laminated ilng stack' 
elements are punched from flat sheet stock of mag- 
netostrictive material, a wasteful pi'ocetlure since the 
rings are quite narrow. Sheet stock could be u.sed 
without waste if it could be cut up into strips as wide 
as the desired wall thickne.ss and the.se strii)s wound 
edgewise to form a ring stack. Some experiments ha\'e 
been i)erformed on the edgewi.se winding of such nar¬ 
row thin strips but with not too succes.sful results. 
Tlie succe.ss of this methofl dej^ends mostly on the 
development of a good edgewise-winding machine. 

13..3.3 Laminated Stack Transducer 
Elements of the Longitudinal 
Oscillator Type 

Wedge-Shaped Type 

The space available for all the jiarts of a single ele¬ 
ment in a scanning sonar transducer has the shape of 
a trajjezoidal prism. To fill this space efficientl.y, the 
active parts of the element should have the same 
trapezoidal section. Elements having this shape are 
shown in Figures 15, Ki, 18, and 19. In elements of 
this type the node is approximately at the center, and 
the outer faces are the loops. The outside face works 
against the acoustic resistance of the water while the 
inside face works against the pre.s.sure-release liacking 
material which, ideally, should i)resent no mechan¬ 
ical load at all. Consequently, except for internal 
energy lo.s.ses in the laminated stack itself, the me¬ 
chanical energy of the vibrating stack is directed into 
the water as sound radiation. This type of element 
makes use of neaily all the active area of the trans- 
ducei' face and conseciuently is capable of radiating 
the maximum amount of power into the water during 
transmission. 

Lamination Design. The jioints that must be taken 
into consideration in the detailed design of a lamina¬ 
tion are: 

1. Diameter of the cylinder formed by the active 
faces of the elements; 

2. Available active face width for each element; 

3. Angle of taper, or number of elements; 

4. Ratio of active face width to total leg width; 


CONFIDENTIAL 
































DESIGN OF VIBKATINi; ELEMENTS 


397 


5. Depth of active face; 

(). Position of node; 

7. Mag:net slot, if the laminated stacks are to have 
jDennanent-inag'net polarization. 

The approximate dimensions for laminations of 
this type are shown for active face diameters of 12 
and 173^^ in. in Figures 40 and 41, respectively. It is 
assumed that the face width of the laminations is 



NUMBER OF ELEMENTS 

Figure 40. .Ajiproximate dimensions of \vedge-.sluii)ed 
scanning .sonar transducer laminations for 12-in. active 
face diameter. 

one-half wat’e length in water, and the leg width is 
one-sixth of this. No allowance is made for space be¬ 
tween adjacent elements oi- for a magnet slot. The 
beam width listed is f s that for the pattern of mini¬ 
mum directivity ratio, as this has been found to be a 
\ alue within practical attainment. It is to be noted 
that for a given number of elements the dimensions 
I'ary directly and the frequenc,y inversely as the di¬ 
ameter of the transducer. Al.so, for a given number 


of elements, the beam width is indejiendent of the 
diameter. 

To derive the exact dimensions of the lamination 
it is suggested that the following j^rocedure lie used. 
First decide on the width of the receiving beam pat¬ 
tern desired and the active face diameter to be used 
(see Figures 40 and 41). These factors determine the 
freijnency and the number of elements which must 



Figure 41. Appro.ximate dimensioas of wedge-shaped 
.scanning sonar transducer laminations for 1734-ui. 
active face diameter. 


be used. About 0.030 in. to 0.050 in. space should be 
allowed between adjacent elements. This determines 
the face width, b. To get a mechanical Q of about 12, 
the width of the legs and the minimum depth of the 
face section should be about one-sixth the face width. 
The Q can be adjusted by varying the ma,ss of the 
face and the stiffne.ss (width) of the legs. This will be 
discussed in .some detail later. The length of the legs 
.should then bo calculated by one of the methods out- 


CONFIDENTIAL 






























































































TIIKOKY AM) I)KSI(;N OK MAtiNETOSTKICTION SCANNIM; SONAK TUANSDUCEKS 


:m 


lined below. The .sum of the faee depth and the leg 
leng:th sul)traeted from the radius of the active fa(*e 
circle g:ives the radius of the nodal line (see Fig¬ 
ure 42). The length of the tapered tail .section must 
he effectively one-fourth wave length in the lami¬ 
nation. However, due to the fact that the tail section 
is tapered, the distance from the node to the loop is 
greater than one-fourth wave length as measured in 



Figure 42. Some geometrical relationship.s to be con¬ 
sidered in the design of tapered laminations for scan¬ 
ning sonar transducers. 


a bar of uniform cro.ss section. The calculation of this 
distance will be considered in detail later. 

The distance from the front face of the lamination 
to the node may be calcidated by the mechanical 
impedance method or by the “spring-and-mass” 
method. In either ca.se, the front half of the lamina¬ 
tion is con.sidered to have the equivalent simplified 
form shown in Figure 43. The mass of the face por¬ 
tion includes some of the arch portion, so that the 
effective mass is about 20 per cent greater than that 
included in the thickness y. Allowance should also be 
made for the taper of the face portion. If 5 is the 


amount of taper on one edge of the face, as shown in 
Figure 43, the average span of the face section is 
(b — 5). The total effective ma.ss of the face portion 
then becomes 

M = ptib - 5) \.2y, (9) 

where p is the density and i is the thickness of the 
lamination. The effective length of the leg portion is 
as .shown in Figure 43, i.e., 

L = d - \.2ij. (10) 

In the mechanical impedance method, the leg por¬ 
tion is ti'eated as a mechanical transmission line 



PdouRE 43. Equivalent .simplified form of the front half 
of a tapered scanning .sonar transducer lamination. 


which is terminated by an infinite ma.ss on one end 
anti the face mass at the other. If this mechanical 
transmission line is to resonate in its first mode of 
vibration, the fretjuency must be such that the me¬ 
chanical impedance at the one end is infinite and at 
the other end is —j2irfM (i.e., mechanical stiffness 
reactance). If the distance x is mea.sured along the 
length of the legs from the node, the mechanical im¬ 
pedance is given by the expression 


CONFIDENTIAL 















































DESIGN OF VIBRATINC; ELEMENTS 


399 


A'm = —jpc2wt cot — -X , (11) 

c 

where c is the velocity of sound in the lamination 
material. The first \’alue of x that makes ecjual 
to 2TvfM at the desired frequency is the proper length 
of the legs, L. This can be simplified to the expression, 

1 ^ ^ ,r 

- • ( 12 ) 

2irf L\.2ivfy {b - 6)J ^ ’ 

1 he total distance from the lamination face to the 
node is, then, 

(I = L + L2y, (13) 

and this determines the position of the nodal line 
relative to the center of the transducer. 

The velocity of sound, c, in magnetostrictive ma¬ 
terials depends upon the state of anneal and the de¬ 
gree of magnetic polarization. Consequently, to de¬ 
termine the lamination dimensions that are required 
to give some nominal frequency of mechanical reso¬ 
nance, it is necessary to know the velocity of .sound 
in the material under its specific conditions of anneal 
and polarization, f’or nickel which has been o.xide- 
annealed at 900 C and which is polarized to approxi¬ 
mately 4,000 gausses, the velocity of .sound is about 
4.75 X 10^ cm per sec and the Young’s modulus is 
about 2.00 X 10'- dynes per sc[ cm. However, it can 
be shown theoretically that the frequency of maxi¬ 
mum efficiency (which is always a little higher than 
the freriuency of mechanical resonance) remains the 
same regardless of the degree of magnetic polariza¬ 
tion. This freciuency is related to the Young’s modu¬ 
lus of the unrnagnetized lamination material. In 
many resjjects it is more logical to design laminations 
for a nominal frecpiency of maximum efficiency be- 
cau.se this frec|uency is independent of the degree of 
)X)larization, because the maximum efficiency of 
transmission is obtained at this frequency, and be¬ 
cause the maximum recei^dng response is obtained 
at this frecpiency when the transducer element is 
terminated in its conjugate impedance. The Young’s 
modulus of imiDolarized, oxide-annealed nickel is 
about 2.10 X 10'- dynes j^er sq cm, and the corre- 
s))onding velocity of .sound is 4.85 X 10^ cm per sec. 
If these values and the nominal frequency of maxi¬ 
mum efficiency are used in equations (9), (12), (14), 
and (15), the jjroper dimensions will be obtained for 
laminations ha^’ing the desired frequency of maxi¬ 
mum efficiency. However, since the shape of lamina¬ 
tions of this type is so complicated that the actual 
freciuency of a given lamination may differ from the 


calculated value by as much as 5 per cent, the above 
distinction may be of little importance from a practi¬ 
cal standpoint. 

In the ,si)ring-and-ma.ss method, the frequency of 
the front half of the lamination is taken to be 


/ = 

2wf (4/ + Km) 


(14) 


where K is the static spring constant of the ecpiiva- 
lent single lc*g, M is the maiss of the face section, and 
m is the mass of the equivalent leg .section. The sjjring 
constant is given by 


K = 


E2u'( 

~ir’ 


(15) 


where E is the Young’s modulus for the lamination 
material and the other ciuantities are as shown in 
Figure 43. If this value for K is u.sed, together with 
the other values as given in Figure 43, the freciuency 
becomes 


f = 


Ew 


27rLpT[0.60y(5 — 5) -f- y^wE}. 


(lb) 


and the length, from this, is 


L = 


0.90y{b - 5)Y 


V 0.75E~ 

/ -^ 

/ PTT-J- J 


0.90.(/(6 - 5) 


(17) 


The distance between the node and the loop at the 
end of the tapered tailpiece may be calculated from 
the radius of the nodal line and the velocity of .sound 
in the lamination by the following relation between 
the Bessel and Neumann functions of the zero and 
first orders, 

Mk-r) ^ J,{kr') 

N,{kr) Nfkr') ^ ^ 


where r and r' are the radii of the node and loop, re- 
.s])ectively. Figure 44 gives a curve showing the re¬ 
lationship between kr and k{r — /•'), where k is the 
wave number, 2ir/\ = 2irf/c. The two radii, r and r', 
are mea.surecl outward from the point of convergence 
of the edge lines of the tapered lamination. Because 
of the spaces between neighboring laminated stacks, 
the point of convergence of the extended outside 
edge lines of the laminations does not coincide with 
the center of the transducer, 0, but falls a little di.s- 
tance out from it, as .shown in the point O' in Fig¬ 
ure 42. In this ca.se, in which the lamination has no 
magnet slot, the distances r and r' would be taken 


CONFIDENTIAL 


















KH) 


TiiKORY AM) i)Esh;n OF MA(;netostri(:tion s(:annin(; sonar transducers 


as O'N and O'B rcsi)ectively. If the lamination does 
have a inajjinet slot, the extended edge lines of each 
half of the tail section have sei)arate convergence 
points near 0", as shown in Figure 42. In this case 
r and r' are taken as 0"N and 0"B respectively. 



In the design of the face section of the lamination 
it is important to make it stiff enough so that all 
imrts of the face move as a single piston when it is 
working against the stiff water load. The parts of the 
face section that extend beyond the region of direct 
support by the legs should be tlesigned so that their 
frequency of vibration as a cantilever beam in the 
plane of the lamination is at least four times the fre¬ 
quency at which the lamination is to operate. C'on- 
sider, for example, the “ears” on the lamination 
shown in Figure 43. The natural frecpiency of vibra¬ 
tion of this as a cantilever beam is ai)proximately 




(19) 


If b is about 1 in., and y and z each about in., this 
frequency is of the order of 200 kc, which is suffi¬ 
ciently high for a 26 kc lamination. 


The stiffness of the ears on the face section must 
l)e great enough to provide the necessary force 
against the radiation resistance of the water with a 
deflection which is small in comparison with the 
amplitude of the face. If the ear is considered as a 
cantilever beam, as shown in Figure 43, the maxi¬ 
mum deflection due to the radiation load is 


_ pccoz* _ 37rpc2‘ 

^ “ Ey^ “ ’ ( 20 ) 

where Vn is the maximum velocity amjflitude of the 
face, .4o is the maximum am])litude, and pc is the 
specific acoustic resistance of water. The ratio of 
f/,nax to *4o should be of the oi'der of 0.1 or less. As an 
example of this, the ears on the lamination of the 
IIP-3 type shown in Figure Ki have a dmax h4o ratio 
of 0.018 at 26 kc. In this case, at atmospheric cavi¬ 
tation pressure in water (i.e., 10'’ dynes per s(i cm) 
the rms displacement amplitude of the face is 
4 X 10“^ cm, so the deflection of the ear is about 
7 X 10“^ cm. 

For some applications it may be desirable to de¬ 
sign laminations which have higher or lower Q’s than 
those which are suggested in Figures 40 and 41. To 
change the Q without altering the frequency it is 
necessary to change the width and length of the legs 
and the depth of the face section. Since 


and 


Q 


A' M + 


III 


bpc 


27r/ = 


,/ A 



( 21 ) 


( 22 ) 


(where A, M, and m refer to a unit height of stack), 
it is necessary to decrea.se both A and M if the Q is 
to be decreased without change of frecpiency, and 
vice ver.sa. The relations between the Q, the face di¬ 
mensions, and the leg dimensions are shown gra])hi- 
cally in Figure 45. These Q’s are based on the assumi)- 
tion that all the damping of the laminated stack is 
due to acoustic radiation resistance on the active 
face. Actually, in any practical laminated stack, 
there is some internal mechanical damping in the 
stack. The amount of this internal mechanical damj)- 
ing can be determined by measuring the Q of the 
laminated stack when the active face of the stack 
has no mechanical load on it. This is u.sually done 


CONFIDENTIAL 




























































DESIGN OF VlBUATlNi; ELEMENTS 


101 


l)y measuring; the Q when the stack is in air, and the 
Q under these circumstances is usually referred to 
as Qa- The corresponding; Q when the laminated 
stack is loaded with water is usually referred to as 
Qn-. The relationship between these Q’s and the 
theoretical one is 


Qw = 


QQa 
Q + Qa 


(23) 


If the tail i)ortion of the lamination is not so massive 
as that shown in Fig;ure 45, as is the case for tapered 
laminations with magnet slots, the Q’s are higher 



Figure 45. Relations among Q, face dimensions, and 
leg dimensions of laminations of the type shown. 
(Curves are a plot of 2Airfy'c versus 2w 6.) 


than those intlicated in the graph but less than twice 
as great. For laminations of the type illustrated in 
Figure 19, the ideal Q's should be about 1.4 or 1.5 
times those shown in Figure 45. 

Polarization. It will be instructive to consider at 
this point some of the detailed characteristics of the 
])olarization of tapered laminated stack elements for 
use in scanning sonar tran.sducers. 

Some typical tapered laminations are shown in 
Figure 4(1. The HP-1 and HP-2 types were designed 
to be polarized by a component of direct current in 
the windings, while the HP-3 and HP-8 types were 
designed to be polarized by permanent magnets. The 
most active portion of these laminations is in the 
legs, especially at the base of the legs near the nodal 
jioint where the mechanical strain is the greatest. It 
is therefore important to have the necessary amount 


of polarizing flux running parallel to the axis of strain 
in the legs. 


(r\ 

O 




y 


J 


■ O- 







Figure 46. Typical tapered lamination form.s for u.se in 
scanning sonar transducers. 


The production of the desired flux density of 3,800 
to 4,000 lines per sq cm in the d-c polarized units 
requires about 40 oersteds of magnetizing field (i.e., 
about 80 amj) turns j^er inch of magnetic path length) 
if the laminations are made of oxide-annealed nickel. 
The length of the magnetic path for laminations of 
this type is very nearly 2.5 times the leg length. Thus 
the total numlier of ampere turns needed is 200L, 
where L is the leg length in inches. The determination 
of the number of turns and size of wire to use in 
winding a stack of laminations of this type should be 
based upon the source of polarizing current, the de¬ 
sired a-c impedance, and the available space for 
windings in the laminated stacks. In the polarizing 
current circuit, isolating choke coils must be used for 
each element of the transducer to prevent the alter¬ 
nating-current path through the transducer elements 
from being shunted by the source of the direct 
current. 


CONFIDENTIAL 
























































































402 


THKORY AM) I)ESK;N OF MV(;\Er().STRi(:TION scawina; sonar transducers 


A typical polarizing circuit for use with a 3()-elc- 
meiit (1-c polarized scanning sonar transtlucer is 
shown in Figure 47. In this case the polarizing cur¬ 
rent was passed through the gi’oup of 18 even ele¬ 
ments in parallel and then through the group of 18 
odd elements in parallel. The polarizing current was 
]n-ovided by a large commercial copper-oxide rectifier 
with filters to smooth out any a-c ripple. The total 



-DC 

Figure 47. Typical polarizing-current circuit for a 
scanning sonar transducer (36 elements). 

power loss in the d-c polarizing current circuit was 
about 550 watts. This loss was divided about ecpially 
between the 36 chokes and the 36 transducer ele¬ 
ments. Also, during the jtinging interval approxi¬ 
mately half of the a-c input power was di.ssipated in 
the input chokes and polarizing chokes together. 
Both these d-c anti a-c power los.ses coukl be elim¬ 
inated by making the transducer elements polarized 
by permanent magnets. In addition, the electric 
netwoi’k a.s.sociated with the transducer is simplified 
\'ery considerably. For this reason scanning sonar 
transducers with elements that are polarized with 
permanent magnets are preferred. For comparison 
with Figure 47, the electric network associated with 
a transducer polarized with j^iermanent magnets is 
shown in Figure 48. 

There are several ways in which laminated stacks 
made of tapered laminations can be polarized by use 


of permanent magnets. However, only about four of 
these ways are practical in terms of the available 
space, available magnetic materials, andiierformance. 
Of these four methods, the one that makes u.se of 
sintered-oxide magnets has ])ro\'ed to be the most 
practical. 

One method of polarizing laminations of the HP-2 
type shown in Figure 4(5 is to make the laminations 
from a bimetal .sheet in which the uj)per half of the 
stri]) is of nickel and the lower half of C’unico. Cunico 



• GROUND COIL 

Figure 48. Typical electric netwurk a.ssociated with 
a .scanning sonar transducer with elements polarized by 
permanent magnets. 

is a copper-nickel-cobalt alloy made by the General 
Electric C’ompany which can be heat-treated to be 
malleable enough to roll into thin sheets and later 
heat-treated to develop magnetic hardness. It is 
possible to butt-weld a block of nickel and a block 
of C’tinico, edge to edge, in a huge s])ot-welding ma¬ 
chine. These blocks can then be rolled to the desired 
thickness so that half the width of the strip is of 
nickel and the other half is of Cunico, with a sharp, 
straight line of demarcation between the two metals. 
The laminations are then punched from this bimetal 
strip so that the face and leg sections are of nickel 
and the base portion of Cunico, with the line of de¬ 
marcation at the lia.se of the legs. .After the lamina¬ 
tions are punched, they are heat-treated to harden 
the Cunico. Fortunately, the hardening tieatment 
for the Cunico .simultaneously anneals the nickel 


COXFIDEXTIAL 













































DESKJN OF VIBKATINC; ELEMENTS 


part. The lamination.^ are then a.s.semhle(l into -stacks 
and mafinetized in sucli a manner that a North pole 
is located in the C'unico at the base of one leg, and a 
South pole at the base of the other leg. This can be 
accomplished best by pa.s.sing a heavy coppei' bus bar 
through the center slot and pas.sing a i)ulse of direct 
current through it large enough to produce a mag¬ 
netizing field strength of 2,500 to 3,000 oersteds in 
the Cunico in the region of the ba.se of the legs. 

The electric and magnetic characteristics of C’unico 
after it has been heat treated for magnetic hardness 
are about as follows: 

//max = 3,200 oersteds, 

/^max = 8,000 gaus.ses, 

B,. = 3,400 gausses. 

He =710 oersteds, 

~ 2.5, 

(/?d//rf),„ax = 0.85 X 10’‘ ergs per cubic cm at 
Hd ^ 420, 

Density = 0.30 lb per cubic in. or 8.3 g per cubic 
cm, and 

Resistivity = 32 X 10“'* ohm-cm. 

A magnetomotive force of about 350 gilberts is re¬ 
quired to produce a flux density of 4,000 gau.sses in 
the magnetic circuit consisting of the two legs and 
face arch of the oxide-annealed nickel HP-2 lamina¬ 
tions, as shown in Figure 4(). The average length of 
the flux path in the Cunico .section below the legs is 
about 1.5 cm, .so that the average demagnetizing 
force in the Cunico due to the opposing magneto¬ 
motive force in the nickel is about 105 oersteds. This 
demagnetizing force reduces the flux density in the 
Cunico to al)out 3,000 gausses. However, because of 
the flaring of the legs at their bases the jmle face area 
of the Cunico is about 1.3 times the cro.ss section of 
the nickel legs, and comsecpiently the flux den.sity in 
the nickel should be nearly 4,000 gau-sses. 

The a-c flux path in the Cunico is estimated to have 
at)out one half as much magnetic reluctance as the 
flux path in the nickel. The eddy-current shielding 
and a-c power loss in the Cunico ]3oi-tion of the mag¬ 
netic path is quite small because of the thin lamina¬ 
tions, relatively high resisti\-ity, and low a-c perme¬ 
ability. 

A small .sample stack of this type was constructed 
and subjected to electrical measurements. No acou.s- 
tic tests were made because the stack face was too 
small to gi^’e the acoustic loading necessary for such 
tests to have any meaning. The electric tests showed 
that the Cunico magnet gave an e(iui\'alent magnetiz¬ 


40:$ 


ing field of about 15 oersteds in the nickel legs, ddiis 
corresponfls to a total magnetomotive foi'ce of about 
150 gilberts, which is le.ss than half what it should be. 
The electromechanical coupling coefficient was about 
0.10, whereas it should have been at least 0.15. This 
low coefficient was due to insufficient polarization 
and to the relatively high reluctance of the magnetic 
])ath in the C'unico section of the stack. The.se facts, 
together with the difficulty and expense of producing 
the bimetal .strip from which the laminations must be 
I)unched, make this type of ijolarization less de.sirablo 
and le.ss efficient than .some others. 



Figure 4!). Tapered, laminated tran.sducer stack 
polarized by a laminated Cunico magnet in a tail slot. 

The second method of polarization by permanent 
magnets also makes use of laminated C'unico. This 
method is illu.strated in Figure 49. The magnet is 
made iqi of a consolidated stack of C’unico lamina¬ 
tions of a ])roper thickness to keejD the eddy-current 
los.se.s to a low value. The thickne.ss of the lamina¬ 
tions should be such that their characteristic eddy- 
current frequency is higher than the operating fre- 
cjuency. A graph showing the characteristic fre¬ 
quency of C’unico as a function of the lamination 
thickne.ss is given in Figure 50. For e.xample, if the 
oiierating frequency is 20 kc, the thickness of the 
C’unico magnet laminations should be less than 
0.050 in. 

The jiroper dimensions of the magnet .slot and 
magnet must be determineil by consideration of the 
magnetic circuit and the characteristics of the mag- 


C’ONFIDENTIAL 

















i04 


THKOKY AND DESKiN OF MAGNETOSTKICTION SCANNIN(; SONAR TKANSDUCERS 


net material. First, the d-c magnetic j^ath may be 
considered as being made up of two parallel paths 
NFS and NGS (see Figure 49). The average length of 
the path NFS is about 2(L + ^) + b 2. To maintain 
a flux density of 4,000 gausses in this path reciuires a 
magnetizing field strength of 40 oersteds, which when 


sectional area of the magnet which must jn-ovide this 
flux is ht. If the flux density in the magnet is B„, the 
total flux of the magnet is Bmbt, and this must be 
ecjual to (),000»’b Therefore, 


h 


(),000(r 


B 


m 


(25) 



.005 .01 .03 ai 0.3 

lamination Thickness in inches 


Figure .50. Eddy-current parameter diagram for 
Cunico permanent-magnet alloy, 2V-Permendur and 
oxide-annealed nickel. 


summed along the jTath adds up to a total magneto¬ 
motive force of 40[2(L 4- y) + 6/2] gilberts. This 
causes a demagnetizing field in the magnet which has 
the value 


Ih 


mmf 

9 


40 


2(T + ^) + - 


oersteds. 


(24) 


The magnetic reluctance of the circuit NGS is diffi¬ 
cult to estimate, but it is found to be roughly twice 
that of NFS. Hence, since the same magnetomotive 
force is applied to both circuits, twice as much flux 
will pass through the NFS circuit as through the 
NGS circuit. The total flux through the NFS circuit 
is 4,000w’f, and hence the total flux which must be 
provided by the magnet is about G,000«’f. The cro.s.s- 


The value of B„, for the magnet is determined from 
the demagnetizing force on the magnet and the mag¬ 
net characteristics. The demagnetization curve for 



Figure 51 . Nominal demagnetization curve for Cunico. 
ttmax = 3,200, Ztmax = 8,000. 


Cunico is shown in Figure 51. The magnet gap width 
g should be made as small as po.ssible, but not .so 
small as to make Hd exceed about 500 oersteds. 
Actually, in laminations of the type shown in Fig¬ 
ure 49, the narrow space available for a magnet slot 
makes it nece.ssary to u.se an Hd of fully 500 oersteds. 
Referring to Figure 51 again, it is found that the 
magnetic flux density corresponding to Hd ecpial to 
.500 is about 1,000 gaiusses. Thus the height of the 
magnet shoukl be about 4 to 5 times the leg width w. 
The line B^O indicates the line of magnetic ecpii- 


('(JNFIDENTIAL 











































DESIGN OF VIBRATING ELEMENTS 


librium of the C'unico magnet while in the nickel 
stack. That is, if the magnet is magnetized fully 
while in the stack and then gradually demagnetized, 
its magnetic state will follow the line B„X). Likewise, 
if the Cunico is not magnetized fully in the beginning, 
its magnetic state will follow a line similar to B/BJ 
as the external magnetizing field is removetl and 
finally settle at the value BJ. 

The a-c magnetic reluctance of the magnetic cir¬ 
cuit is the sum of that of the nickel path and of the 
magnet and air-gap i)ath. To give an idea of the 
I'elative magnitudes of these reluctances, those for 
the design shown in Figure 49 are 1.0(i for the nickel 
path and 0.075 cgs units for the gap path. This .shows 
that only about 7 per cent of the total a-c reluctance 
is contributed by the gap path. This means that the 
insertion of the gap and the magnet does not greatly 
alter the a-c magnetic characteristics from those of a 
solid, d-c polarized type of lamination. 

Two .sample stacks of this type were constructed, 
using modified laminations of the HP-2 form shown 
in Figure 46. The laminated Cunico magnets were 
cemented solidly in place in the slots. The electrical 
measurements showed that the stacks were .some¬ 
what underpolarized for maximum efficiency and 
that the presence of the magnets and magnet slots 
disturbed the frecjuency of re.sonance and tended to 
cause multiple resonances. It was learned later that if 
the magnets are not cemented to the stacks most of 
the variations in the frequency of resonance can be 
eliminated. The polarization can be increased by in¬ 
creasing the height of the magnet. Acoustic tests 
showed the same characteristics of the stacks as did 
the electric tests. The efficiencies of these experi¬ 
mental stacks were of the order of 20 per cent. 

A third method of polarization, which does not 
require the u.se of polarizing current, provided the 
stacks are not driven harder than 15 oersteds of peak 
magnetizing force, is to make the entire laminations 
of 2^'-Permendur and operate them at magnetic 
remanence. The chief objection to this method is the 
l)resent high cost of 2\'-Permendur. 

If 2\'-Permendur is u.sed, the thickne.ss of the 
laminations shoidd be selected on the basis of the 
curve shown in Figure 50. For example, for 26-kc 
oi^eration the laminations .should not be thicker than 
0.020 in., and the strij) from wliich they are jiunched 
should be hard-rolled. The laminations should have 
the general shape of the HP-2 tyjie shown in Fig¬ 
ure 46. After they are punched, they .should be an¬ 
nealed at 500 to 525 C' in a hydrogen atmosphere 


40.5 

to give the following appro.ximate magnetic char¬ 
acteristics : 

At //ma.x ~ 100 oersteds, 

Bnxax ~ 20,500 gausses, 

Br ~ 17,000 gau.sse.s, 

He ~ 27 oersteds, 

Mr ~ 55. 

Stacks made of laminations of this kind should be 
callable of producing sound pressures at the active 
face of considerably more than lO** dynes per sq cm 
without danger of magnetic depolarization. However, 
care would have to be taken that the peak values of 
any currents (transients included) in the windings 
should not exceed the value which would produce a 
magnetizing field of 15 oersteds in the legs. 

The fourth and most successful method of polariza¬ 
tion by permanent magnets makes u.se of sintered- 
oxide magnets. The.se are used in the same way as 
the C'unico, as .shown in Figure 49. Sintered oxide is 
an oriented magnetic material supplied by the Gen¬ 
eral Electric C'ompany. The desired direction of mag¬ 
netic polarization must be specified to the manufac¬ 
turer .so that the material can be heat-treated in a 
magnetic field in the proper direction. The character¬ 
istics of sintered oxide are about as follows (the mag¬ 
netic characteristics refer to the jirincipal axis of ori¬ 
entation) ; 

At //max ~ 4,000 oersteds, 

B,xxax ~ 6,400 gau.s.se.s, 

Br ~ 1,800 gau.sises. 

He ~ 1,000 oersteds, 

Mr ~ 115, 

(/L//<i)max 0.7 X lO-' at Hd = 700, 

ResLstivity csi 10'’ ohm-cm, and 

Den.sity 0.13 lb per cubic in. or 3.(5 g per cubic 
cm. 

The high re.sisti\'ity of this material makes it un¬ 
necessary to laminate it to reduce eddy-current losses 
at high frecpiencies. In fact, it is .such a good insulator 
that these lo.sses in it are entirely insignificant. Be- 
cau.se of its high coercive force, the tlimensions of the 
magnets in the direction of magnetization can be 
made quite small, a great advantage in this applica¬ 
tion since it is desirable to keep the magnet slot as 
nai'i'ow as |iossibIe. 

The design jirocedure for magnets of this type is 
the same as that described above for Chmico mag¬ 
nets. The demagnetization diagram for sintered 
oxide is shown in Figure 52. The magnet slot in this 


C(4NFIDEXTIAL 



106 


THEORY AM) HESKiN OF MAGNETOSTRICTION SCANNINti SONAR TRANSDUCERS 


case .should he kept wide enough to make the de¬ 
magnetizing force on tlie magnet less than 700 
oersteds. 

If de.sign calculations of this type are made for a 
lamination of the size and shape shown in Figure 49, 
with a magnet slot width of in. ami a flux density 
of 4,000 gausses in the legs, the demagnetizing field 
on the magnet itself is about 700 oensteds, and the 
height h of the magnet is about 2.5 cm. This indicates 
that the magnet should fill about half the slot. 



H IN OERSTEDS 

Figure 52. Xominal demagnetization curve for sintered 

oxide, //max — 4,000, Bmvi\ ~ 0,400. 

Actually it was found by experiment that the flux 
leakage is greater than that estimated and that the 
flux density at the bases of the nickel legs should l)e 
made a little higher than 4,000 gau.sses. These effects 
make it neces.sary to fill the entire slot with magnet. 
To eliminate any effects on the vibration character¬ 
istics of the stack, it was found necessary to grind 
the magnets to a thickne.ss that allowed them to 
slide freely in the slot. The magnets should never be 
cemented or bonded directly to the stack in any wajv 
The most important re.sults of measurement on this 
type of stack will be presented here to illustrate their 
various properties. 

The stacks used in the tests were maxle of oxide 
annealed 0.01-in. nickel laminations (unle.s.s other- 
wLse specified) cemented together with C-3 Cycle- 
Weld resin. The stacks were 3.75 in. high and were 


wound with the standard 37H-turn winding (19 turns 
on one leg and 18^ turns on the other). In addition 
to the regular windings, search coils were wound on 
the legs at the places indicated in Figure 53. A .search 
coil was also wouml around the peripheiy of the 
sintered-oxide magnet to measure flux changes in the 
magnet itself. The magnets wei'e magnetized while in 


FACE ARCH 



Figure 53. Diagram .showing various positions of 

.search coils u.sed in making flux tests on 11 P-3 stacks. 

place in the nickel .stacks by jtlacing the entire .stack 
a.s.seml)ly in a sitecially shaped jig between the pole 
pieces of a large electromagnet. The magnetizing 
field in the gap was about 3,000 oersteds. 

The flux densities in tlifferent parts of the legs were 
determined by measuring the flux change in the vari¬ 
ous search coils when the sintered-oxide magnet was 
.suddenly withdrawn, and adding to this value that of 
the remanence flux which was determined by sud¬ 
denly removing the search coil from the stack after 
the magnet hail been withdrawn. Two sets of values 
of flux are specified, viz., those determined during the 
first withdrawal of the magnet and those determineil 
after the magnet has been in.serted and withdrawn 
from the slot several times. The magnet is slightly 
depolarized liy pulling it out of the .slot into the air 
where the demagnetizing effect of its own external 
magnetic field is greater than it is in the nickel yoke. 
Thus, when the magnet is in.serted in the slot again 
the flux produced in the nickel legs is slightly less 
than the initial value. These two values are referred 
to as initial and steady-state A'alues. 

Figure 54 shows the measured flux densities 
jjlotted against the position in the legs. The lamina¬ 
tions annealed in hydrogen show the highest flux 


CONFIDENTIAL 





















































DESIGN OF VIBRATING ELEMENTS 


107 


densities because of their greater d-o permeahilit 3 ^ 
The curves shown in dotted lines refer to a special 
stack made in short sections l)ut having the same 
height as the standard ones. The lower solid curves 
refer to a standard stack. Magnets of different thick¬ 
ness were used in this latter stack to determine the 
effect of making the magnet tlunner than nece.s.sary. 
The nominal width of the magnet slot was 0.188 in., 
hut because of irregularities in it the thickest magnet 
that could be used was 0.180 in. The thinnest magnet 
used was 0.150 in. The Mux density produced in the 
legs by the 0.150-in. magnet was about 12 per cent 
le.ss than that produced l)y the 0.180-in. magnet. This 



0 0.25 0.50 0.75 I 1.2 5 1.50 

node distance from node in inches face 

I ARCH 

I 

Figure .54. Flux density in the legs of HP-3 stack. 

degree of variation in the polarization would produce 
an unsatisfactory amount of variation in the im¬ 
pedance of the elements; the thickne.ss of the magnets 
should therefore be held to much clo.ser tolerances. 
All the flu.x-density curves show that a considerable 
fraction of the flux leaks acro.ss from one leg to the 
other before the face arch is reached. This has very 
little detrimental effect as far as the magnetostrictive 
action is concerned becau.se the most important re¬ 
gion is that near the node where the flux density is 
maximum. This does indicate, howevei', that the 
coils should be kept as near the node as possible so as 
to link the maximum of a-c flux dui’ing receiving or 
transmitting. 

The magnetization curve for a .samjjle of General 
I']lectric No. 50 sintered oxide is shown in Figure 55, 
in which dir/ = B-H is plotted against //. After the 


material is magnetized the removal of the magnetiz¬ 
ing field causes very little decrease in the degree of 
magnetization. This effect is shown in Figure 50 for a 
.sample of GE No. 1.32 sintered o.xide. This means 
that after the material is magnetized the major jjart 
of the change in flux density in the magnet is the 
magnetizing field itself and not the change in 4x7. 
This effect is illustrated in Figure 57, which shows a 
family of demagnetization curves (/? vs 77) and some 
minor hysteresis loops. 

The magnetic state R shown in Figure 57 is reached 
by removing the magnetizing force after the magnet 
has been magnetized in a close-fitting iron yoke. The 



H IN OERSTEDS 

Figure oo. Magnetization curve for sintered oxide. 

magnetic state .4 is reached from the state R by pull¬ 
ing the magnet out of the iron yoke into the air. The 
state R' is reached from the state .4 by inserting the 
magnet into the iron yoke again. The magnetic 
cycle AR'A can be repeated any number of times 
without change. If the same magnet is magnetized 
while in place in a nickel stack it comes to equi- 
lil)i-ium in the magnetic state S. If then the magnet 
is removed from the nickel stack, it drops to the mag¬ 
netic state .4. When it is reinserted in the nickel stack 
it goes up to the state S'. The cycle TS'A can be re¬ 
peated any number of times. The slopes of the minor 
hysteresis loops show the reversible permeability of 
.sintered oxide to be about 1.15. The line SS'O is the 
locus of the state of magnetic eiiuilibrium of sintered- 
oxide magnets in HP-3 nickel stacks. The line AO 
is the corre.sponding eijuilibrium line for the .same 
magnets in air. 


CONFIDENTIAL 





































































408 


THEORY AND DESIGN OE MA(;NEr(>STKIGTION SCANNINi; SONAR TRANSDUCERS 


If the magnet has been newly magnetized in the 
nickel stack and is initially in state S and an alter¬ 
nating magnetizing field applierl to it (as would be 
the case if alternating current were passed through 
the windings of the stack), then on the first (piarter- 
cycle in the demagnetizing direction the state of the 
magnet would move to 1 ) and from then on it would 
follow the stable minor hysteresis loop DS"E. The 
slight demagnetization caused by such treatment is 
beneficial because it puts the magnet in a stable state 


passing a 15-amp (peak) current through the wind¬ 
ings. After the equilibrium state had l)een reached, 
the flux changes produced by positive and negative 
currents of 3, (i, 9, and 12 amp were measured. In 
Figure 58 it will be noticed that the depolarizing cur¬ 
rents produce much greater flux changes in the mag¬ 
net than do the magnetizing currents. This is at¬ 
tributable to the fact that flux den.sity in the nickel 
is .so great in the first place that a large magnetizing 
foi’ce is reciuired to increa.se it, whereas if the current 



H IN OERSTEDS 

Fige're .56. Dc'magnetization curve for sintered oxide. 


of equilibrium from which it cannot be disturbed by 
the alternating current during pinging, unle.ss this 
driving current shoidd exceed the current used in the 
initial stabilization. It is interesting to note that be¬ 
cause the left portion of the equilibrium curve SS'O is 
quite flat, the magnet can t)e depolarized a consider¬ 
able amount without any .significant decrease in the 
flux density of the magnet or of the nickel legs. 

The depolarizing effects of very large currents in 
the windings of the nickel stacks were in\Tstigated 
quantitatively by observing the changes in flux 
through the magnet when the direct current in the 
windings of the stack was changed by known 
amounts. The.se results are .shown in Figure 58. The 
states S, A, and Si were obtained in the same manner 
as before, i.e., by removing the magnet from the shA 
and replacing it. The state So was then reached after 
the application of a depolarizing current of 13 am ]3 
through the windings. The state S 3 was reached after 


is in the direction to demagnetize, the permeability 
of the nickel is increased and a larger part of the de¬ 
magnetizing force is effective on the magnet. For ex¬ 
ample, an analysis shows that 30 per cent of the total 
magnetomotive force produced by the op])osing cur¬ 
rent of 12 amp is applied across the magnet, whereas 
it is only 5 per cent for an aiding current of 12 am]). 
(In the HP-3 laminated stacks with 373^ turns, the 
average magnetizing fiekl in oersteds is al)Out 5.4 
times the current in amperes.) 

The total flux in the magnet, in the base of the 
nickel legs, and in the face arch of a standard IIP-3 
stack is plotted in Figure 59 as a function of the 
direct current in the windings. Fi'om this graph the 
amounts of flux k^akage can readily be .seen. Ap- 
pro.ximately one-fourth of the flux of the magnet does 
not enter the base of the leg.'<, and of the amount that 
does about one-fifth leaks acro.ss before reaching the 
face arch. These ratios break down ra})idly when the 


CONFIDENTIAL 



























































DESIGN OF VIBRATING ELEMENTS 


109 


2000 




-1000 -800 -600 -400 -200 

H IN OERSTEDS 


Figure 57. Demagnetization curve and minor hy.steresis 
loop.s for sintered-oxide magnets determined from steel 
yoke and nickel stack measurements. 

average dejtolarizing field in the legs exceeds 20 
oersteds. This graph also shows that the fiux-current 
ratio is reasonably linear only over the range of 
// = +16 oersteds. This is not such a great limita¬ 
tion, however, when it is recalled that at the fre¬ 
quency of resonance a peak current of + 2 amperes 
is sufficient to cause cavitation of the water at the 
active faces of the elements (at atmospheric jires- 
sure). The intercept of the curve on the H axis shows 
that the magnet provides polarization ecjuivalent to 
an average polarizing field in the legs of 45 oersteds. 

The demagnetizing effects on the magnet due to 
vigorous 60-cycle a-c pulsing of an HP-3 stack at 
room temperature (75 F) are shown in Figure 60. 



-lOOC -800 -600 -400 -200 

H IN OERSTEDS 

Figure 58. Minor hysteresis loops for sintered-oxide 
magnets in HP-3 stacks produced by changes in direct 
current in the windings of the stacks. 

The duration of each pulse was about one second. 
The loci of the lower left ends of all the minor hys¬ 
teresis loops nearly coincide with the primary de¬ 
magnetization curve corresponding to the initial 
magnetization. Repeated jiulses at 11.3 amp (peak) 
produced no more demagnetization than the first 
pulse. However, at 14 amp (peak) additional pulses 
produced additional demagnetization until a final 
stable value was reached. The measured values of the 
impedance of the stack at 20 kc Z 20 under the various 
states of magnetization are shown by the scale at 
the left. 

It was found that subjecting the magnets to a-c 
magnetic pulsing while they are hot produces more 
demagnetization than when they are cool. Figure 61 
shows the results for one pulse and 10 pulses at tem¬ 
peratures of 200 F and 300 F. At temperatures above 
300 F, considerable demagnetization is produced by 


CONFIDENTIAL 




































































410 


THEORY AM) DESKJN OF MAIJNETOSTRICTION SCANNIM; SONAR TRANSOICERS 



Figure 59. Total flux in magnet, legs, and face arch of 
an HP-3 stack as a function of direct current in the 
windings. 

relatively small eurrents. The reiluctioii of the co¬ 
ercive force due to increase in temperature makes it 
necesisarv to limit the amplitude of magnetic pulsing 
of the stacks at temperatures above 200 F. The most 
adverse conditions of operation for the magnets 
wotdd be to drive the stacks continuously at such a 
high level that the heat produced by copper losses 
and core losses would raise the stack temperature to 
200-300 F. There is practically no danger of this hap¬ 
pening in a full-sized transducer diT'en by a gener¬ 
ator that derives its energy in pulses from an energj’ 
storage system working on the duty-cycle principle. 

No ob.servable effects on the magnetic properties 
of the sintered-oxide magnets have been fouml as a 
result of soaking them in water, Ucon oil, or castor 
oil. Heating them after they are soaked and ^-acuum- 
impregnating them with resins ha\'e also been found 
to ])roduce negligible effects. The imjjregnation of the 
magnets with such resins as GE Permafil or some of 
the bakelite resins increases their mechanical strength 



H IN OERSTEDS 


z 

(D 


Figure 60. Demagnetizing effect due to 60-cycle a-c 
pulsing at room temperature (75 F.). 


and reduces their jTorosity. There is nothing about 
the mechanical, magnetic, or chemical properties of 
the magnets that should jn’event their use in oil-filled 
or water-filled transducers. 

The scanning .sonar transducer elements that are 
polarized by permanent magnets inserted in the tail 
.section must be placed in the supporting spool so that 
like magnetic poles are adjacent, otherwise the full 
circle of tail sections would form a magnetic short 
circuit around the spool. The flux measurements 
which have been presented in the foregoing material 
were made on single isolated stacks. To find the effect 
on the flux densities of bringing several stacks close 
to each other, three stacks were mea.sured alone and 
then together (j^e-in. spacing). The flux density of 
the magnet in the center .stack of the group decreased 
about 12 per cent, while the flux density in the nickel 
face arch increased about 2 per cent. The fraction of 
the flux of the magnet which passed through the face 
arch increased from 58 to (>7 jjer cent. 

In some scanning sonar transducers the back ends 
of the laminated stacks are .separated from the steel 
core of the spool by only a 3^-in. layer of corprene or 
other nonmagnetic material. The magnetic short- 
circuiting effect of this steel on the magnets in the 
stacks was measured and found to be negligible. 
However, the distance of separation should not be 
made much le.ss than in. 


C(3XFIDENTIAL 


































































DESIGN OF VIBRATING ELEMENTS 


Ill 



i800 


-1000 -800 -600 -400 -200 0 
H IN OERSTEDS 


1000 w 

■D 

< 

O 

800 H 
m 

600 

400 

200 

0 



H IN OERSTEDS 


c/l 

u 

tn 

< 

o 

z 


m 


1800 

1600 

1400 
1200 

to 
to 

1000 < 
o 

800 - 
CD 

600 
400 

200 
0 

-1000 -800 -600 -400 -200 0 

H IN OERSTEDS 



1800 

1600 

1400 

1200 

to 

(O 

1000 < 
O 

800 - 
m 

600 

400 

200 
0 

-1000 -800 -600 -400 -200 0 

H IN OERSTEDS 



Figure 61. Demagnetizing effect due to simultaneous heating and a-c magnetic pulsing. 


SP Type of Laminated Stacks 

The general design of an element made from stacks 
of laminations of the SP type is .shown in Figure 20. 
Some of the advantages of this type of construction 
are: preformed coils can be u.sed on the stacks; the 
elements are made of relatively short sections which 
can be readily adapted to amijlitude shading to pro¬ 
duce minor lobe reduction in the vertical pattern; 
and the individual stacks are so short that no trouble 
should be caused by multiple re.sonances of the type 


that are produced in thicker stacks by too-strong 
consolidation. However, the fact that the active face 
area of the elements made up of SP stacks is less than 
half the available face area causes the mechanical Q 
to be higher than it should be and limits the total 
radiation area. Greater care must be used in aligning 
the large number of small stacks, and the umsup- 
ported spaces of the transducer face between ele¬ 
ments are vulnerable to damage from pre.ssure or 
impact. 


CONFIDENTIAL 





























































412 


THEORY AM) DESIGN OF jMAGNETOSTKIGTION SCANNING SONAR TRANSDUCERS 



Figure 62. kSome general forms of ladder-shaped laminations. 


Lamination Design. The detailed design of lami¬ 
nations of the SP type is very similar to that for 
the wedge-shaped laminations as di.seiissed in Sec¬ 
tion 13.3.3. The only difference is that the length of 
the heavy tail section of the SP laminations is made 
exactly equal to one-fourth wave length because of 
its unifoi’in cross section. Thus the length of the tail 
section is c/4/, where c is the velocity of .sound in 
nickel. 

The mechanical Q of laminations of this type is 
determined as indicated in Figure 45 and as de¬ 
scribed in Section 13.3.3. All other design considera¬ 
tions are essentially the same as those discus.sed in 
Section 13.3.3. 

Stack Mounting and Acoustical Contact. Some 
methods of mounting stacks of the SP type and of 
providing for acoustic contact between the active 


faces of the stacks and the water have been di.scus.sed 
in Section 13.2.3. With the aid of .some imagination, 
a designer can make up ^’ariations of the design 
shown in Figure 20. For examjile, the stacks might 
be cemented to impregnated glass fiber face strii)s of 
the type indicated in Figure 18 and the entire array 
of elements enclosed in a watertight rubber boot. 
If the face strips are sufficiently light and strong, 
they will not influence the frequency very much and 
yet will increase the area of the radiating active face 
by a considerable amount. 

L.A.DDKH-TYPE ELEMENTS 

General Form. The general types of elements 
which can be made uj) of SP-type laminations can 
also be made from laminations ha\ ing the form of a 
ladder. Some general forms of this ty])e are shown in 


CONFIDENTIAL 





































































































i)esi(;n of vibratinc; elements 


413 


fiflure G2. These can be punched in continuous strip 
form by using a die with an accurately indexed feed 
meclianism. A transducer element would be made by 
cutting the continuous strip material into lengths 
corresponding to the length of the element and con¬ 
solidating them to form the comi)lete ladder-shaped 
stack. 

The form shown in Figure G2A is symmetrical, 
with legs of uniform width. Two ways of winding are 
shown.The one on the left is made by threading the 
wire around the legs. This is tedious and time-con¬ 
suming. The one on the right is made by winding the 
coils around powdered iron cores. The windings and 
cores are made .solid by impregnating them with 
some type of resin or cement. Then the preformed 
coil and powdered core assemblies are slipped into 
the slots of the laminated stack. Powdered iron is 
used to reduce eddy-current los.ses. The first method 
of winding gives the best magnetic circuit and the 
greatest electromechanical coefficient, whereas the 
second method is poorer in the.se respects because the 
magnetic flux is not parallel to the mechanical strain 
in the region of the node where the greatest mag- 
netostricti^■e driving force is needed. 

Figure G2B shows a type of lamination which can 
use the preformed coil type of winding without much 
I’eduction in the electromechanical coupling coeffi¬ 
cient and efficiency. This improvement over the form 
shown in Figure G2A results from making the center 
poi-tion of the legs wider in section .so that the region 
of maximum strain is shifted from the nodal point to 
the points where the narrow part of the legs joins the 
wide ))art. At this latter point the direction of the 
magnetic flux is parallel to the direction of mechan¬ 
ical strain. Theoretical calculations show that the 
effecti\T electromechanical coupling coefficients for 
the left- and right-hand ca.ses of Figure G2A and 
case B of Figure G2 are 0.20, 0.08, and O.IG respec¬ 
tively. 

The form shown in Figure G2B can be readily 
polarized by use of sintered-oxide magnet material. 
Since the magnetic j)aths are symmetrical there is 
not so much flux leakage as there is in the ca.se of the 
open-ended wedge-shaped laminations. 

Pdgure G2C shows an a.^jymmetrical form of the 
ladder type of laminations, which has the lowest me¬ 
chanical Q of any of the forms shown. This type must 
be wound by threading the wires through the wind¬ 
ing slots. It must be polarized by u.se of direct cur¬ 
rent in the windings or by using the magnetostrictive 
lamination material at its magnetic remanence. 


The lamination form shown in Figure G2D is a 
hybrid which is stronger and easier to handle than 
the form shown in A. However, it must be wound by 
threading the wire through the slots and must be 
polarized by direct current or magnetic remanence 
flux. 

Design Details. The dimensions recpiired to give 
a desired freciuency in laminations of the form shown 
in Pdgure G2A are determinetl in the same way as for 
the front half of a wedge-shai)ed lamination de- 



Figure f)3. Mechanical impedance along the legs of the 
type of lamination sliown. 

scrilted in Section 13.3.3 The node is taken to be at 
the center of the length of the legs and the dimen¬ 
sions are symmetrical on each side of the node. The 
mechanical Q’s for laminations of this type are ap¬ 
proximately 1.5 times those indicated in Ldgure 45. 

The dimensions that will give a specified freciuency 
for laminations of the form shown in Figure G2B are 
.somewhat difficult to derive because of the change 
in the width of the legs. The most direct method is to 
u.se the mechanical impedance concept. Figure G3 
shows a section of a leg with the amount of the face 
section which is associated with it. A simplified, 
ecjuivalent block section is also shown to aid in the 
calculation. The distance x along the legs is measured 


CONFIDENTIAL 
































TiiEOKY AND desi(;n oe \iacnp:tostricti()n scanning sonar transducers 


III 


from the node toward the face. In a typical design 
the width W2 of the narrow portion of tlie leg is about 
one-third the width of the as.sociated face section b. 
The width lOi of the wide part of the leg is about 
twice that of the narrow part. The ecpiivalent depth 
of the face section is about 1.2 times the dejith y of 
the face arch. If sintered-oxide magnets are to be 
used, the width of the magnet slot must l)e about 
one-fourth the length of the narrow part of the leg, 
and the total length of the magnet slot 2Li must be 
about five or six times the width of the narrow part 
of the leg, W2. 

The lower i)art of Figure (53 shows a plot of the 
mechanical imjjcdance along the length of the legs. 
The mechanical impedance (i.e., force velocity) 
in the wide part of the leg is given by the exjjression 

^Trf 

jwipct cot — -X, (2(5) 

c 

where p is the density, c the velocity of sound, t the 
thickness of the laminations, aiifl / the frecpiency. 
The length of the wide portion of the leg is set by 
the magnetic reciuirement described above, viz., 
Li ~ 3w2. Hence the mechanical imi)edance at the 
junction of the wide and narrow parts of the leg is 
jwipct cot 27r/Li/c. From this {position on out to the 
face block, the mechanical imi)edance is given by the 
expression 

27r/ 

jw 2 pct cot —(.r — x') , (27) 

c 

where x' is determined by the condition that the im¬ 
pedance given by equations (26) and (27) is the same 
at the position Li, that is, 

27r/' 2Trf 

Wi cot —Li = W2 cot —{Li — x') • (28) 

c c 

The end of the effective part of the leg would come at 
the position x = L where the mechanical impedance 
of the leg is eciual to that of the face block, which is 
considered to act as a rigid mass M = \.2yhtp. Thus 
L is given by the relation 

2wf 

jw-^pcl cot — {L — x') = j2TrfM- (29) 
c 

The dimensions recjuired to give a desired fre¬ 
quency for laminations of the type shown in Fig¬ 
ure 62C are determined in the same way as for lami¬ 
nations of the SP type as described in Section 13.3.3. 
The Q’s for laminations of this type are given by the 
graph shown in Figure 45. This type of lamination 
has the disadvantage that there is a large amount of 


mechanical coupling along the length becau.se of the 
transverse stiffness of the deep tail section. Stacks of 
such laminations do not operate well when amplitude 
shading or phasing of the different leg sections is 
applied. 

The calculation of the dimensions of laminations 
of the form shown in Figure (521) is about the same 
as for the type shown in Figure G2B. The width of 
the wide section of the leg in this ca.se is approxi¬ 
mately three times that of the narrow jjart of the leg. 
The “spring-and-mass” methoil (see Section 13.3.3) 
of calculation can also be readily a]){)lied to tins case. 
In .such a calcidation, the “spring” portion would be 
considered as extending from the bottom of the wind¬ 
ing slots nearest the node to within l.2y of the face. 

Ring-Shaped Ladder Type 

General Form. The general form of a ring-shaped 
ladder type of lamination designed for polarization 
by sintered-oxide permanent magnets is shown in 
Figure 27. The “element” con.sists of a pair of ad¬ 
jacent legs in the ring. The node is located approxi¬ 
mately at the middle of the magnet slot and extends 
parallel to the outside and inside faces of the ring. 
The outsifle and inside faces have the maximum am¬ 
plitude of motion. The legs joining the outside and 
inside faces are made wide in the center to improve 
the magnetic circuit and increase the electromechani¬ 
cal coupling as de.scribed above in Section 13.3.3. 
The elements are mechanically coiqjled at the out¬ 
side anti insitle entls but experiments show that the 
coupling is not enough to cau.se trouble in phasing 
and amplitude shading.''*'^ 

Lamination Design. The detailed design of lami¬ 
nations of this kind is somewhat complicated. The 
face width of an element .should be made about etpial 
to one-half wave length just as in other scanning 
sonar transducers, and consetiuently the usual re- 
lationshij) between the number of elements, active 
face diameter, and frequenc^y is applicable. The fre¬ 
quency and active face diameter are chosen on the 
basis of the width of the receiving jiattern desiied. 
After the active face diameter, frequency, and num¬ 
ber of elements have been decided upon, the details 
of the design of the remainder of the laminations can 
be completed. The portion of the active face that is 
devoted to one element can be suiJiiorted by one or 
two legs. The two-legged support fits the require¬ 
ments on the magnetic circuit and magnets some¬ 
what better than the one-legged .support. The design 
procedure which will be pre.sented here will apply to 


CONFIDENTIAL 



DESIGN OF VIBRATING ELEMENTS 


415 


the case of two legs per element. If a design using 
one leg per element is desired the same general 
method can be followed. 


FACE 



Figure 64. One leg of a ring-shaped, ladder-type 
lamination and its simplified equivalent form for use 
in design. 


The RLP-type laminations are jteifectly uniform 
around the ring and the detailed design calculations 
can therefore be concentrated upon one leg and the 
outer and inner face ma,sses which are associated 
with it. It is true that the outer and inner face rings 
contribute some stiffness against which the face 
masses must work (as in a pure annular lamination), 
but this stiffness is small in comparison with the 
stiffness of the legs. For example, in a lamination 
which is 12 in. in outside diameter, 7 in. in inside 
diameter, and designed to operate at 36 kc, the stiff¬ 
ness reactance due to compression and expansion of 
the outer face ring is about 2 per cent of that due to 
the legs, and the stiffness reactance of the inner ring 
face is about 6 per cent of that due to the legs. C'on- 


sequently the freiiuency of resonance should be 
slightly higher than that calculated on the basis of 
neglecting the stiffness of the inner and outer face 
rings. 

Figure 64 shows a small .section of a lamination 
which consists of one leg and the associated face 
ma.s.ses. At the right hand of the same figure a simpli¬ 
fied form of the lamination is shown which is con¬ 
venient to u.se in the design calculations. It is sug¬ 
gested that the following steps be followed in de- 
tei-mining the exact dimensions of the lamination. 

1. To get a mechanical Q of about 10, the face 
depth and the leg width should be made approxi¬ 
mately one-fourth the width of the outer face per leg. 

2. If the face depth ij is about one-fourth the face 
width b, then, becau.se of the ma.s.s of the face arches 
in the actual lamination, the effective mass of the 
outer face section is 


Mic^l.25yb,tp- (.30) 

3. Write the general expre.ssion for the mechanical 
imi)edance of the outer leg .section as a function of the 
distance X 2 measured from »Si toward S 3 : 


= jpctuh tan —(j -2 -b X 2 ), (31) 

c 

where x '2 is given by the condition that the magni¬ 
tude of the reactive impedance of the leg section is 
equal to that of the face block at Si, 


viz.. 


jpCtWi 



j 2 wf{\. 2 bybitp) , 


tan' 


(32) 


, 2 iTf{\.2bybi) 

- 

2irf cWi 

4. The width and length of the magnet slot is de¬ 
termined by the type of permanent magnet to be 
used and by the length and width of the legs of the 
lamination. For sintered-oxide j)ermanent-magnet 
material, the total width of the magnet slot w,,, 
.should be approximately Js'Lo, and the total length 
of magnet slot 2 Li should be about eight times the 
width of the legs Wi. This means that Li ~ 6 be¬ 
cause Wi ~ fe/4. 


5. After Wm and Li are determined, then Wz can be 
exprc.ssed in terms of b, y, Li, and Lo, becau.se the leg 
section has a definite taper determined by the central 
angle 360°/2A’, where N is the number of elements 
or pairs of legs. Thus 


W3 


b — Wm — 2( \. 2 by -f- Ly -|- To ) tan 


=) 


360° 

4 ^ 


(33) 


As b, Wm, Li, and N have already been determined, 
Wz is a function of the \'ariable To alone. 


CONFIDENTIAL 

















































416 


THEORY AM) DESK^N OF MAGNETOSTRICTION SCANMM; SONAR TRANSDLCERS 


(■). The length can now be found by calculating 
the mechanical impedance at S 3 by starting at the 
node and equating this to The value of 0-2 that 
satisfies the equation is the proper value for L-^. If 
the common factor jpct is omitted, this equation is 

360° 


w ?3 + 2 Li tan 


4A" 


, 27r/ 

cot — Li 
c 

‘2.ivf 

= ii \ tan —{Li + X 2 ) ■ 
c 


(34) 


(Strictly speaking, the mechanical impedance in the 
wedge-shaped center portion of the leg should be 
represented by a combination of Bessel and Neu¬ 
mann functions, but the cotangent representation is 
reasonably accurate and more readily solved.) This 
equation can be solved most readily by plotting the 
functions on each side against Lo and noting the 
value of Li at which the two curves intersect. 

7. After Li is found, the numerical value of wz can 
be calculated and the approximate mechanical im¬ 
pedance at 54 can be determined from the expression, 

■ ( 360 °\ 2wf^ 

jpct\Wz — 2 Li tan — ^ j cot — Lr (3o) 

8 . The mechanical imperlance along the inner leg 
can now be written as a function of Xz, the distance 
along the inner leg measured from *84 toward Si. 
This is 

jpctwi cot —{xz 4- 4 - 3 ). (35a) 

c 


where x^ is given by the condition that the mechani¬ 
cal impedances at *84 are the same for both the thick 
and thin sections. Thus 

360°\ 2irf^ 1 
u'z — 2Li tan —— I cot —Li 
4A / c 

U'l 

(36) 

9. The length of the inner leg can now l)e de¬ 
termined by the matching of the mechanical im¬ 
pedance of the leg at its innermost end with that of 
the inner face mass. However, the magnitude of the 
inner face mass also depends upon the length of the 
leg. The easiest method of solution is to plot the 
mechanical impedances of the inner face mass and of 
the leg as functions of Lz and find the value of Lz at 
which the two curves intersect. This is the proper 
value for Lz obtained from the equality: 

27r/ 

j 2 wf{l.loybitp) = jpctivi cot —(Lz -f X 3 ) , 

c 


a-3 = 


27r/ 


cot' 


or 27r/(l. 15 ^ 62 ) = cu'i cot —{Lz 4- ^- 3 ) , (37) 

c 

w here bi = u'z 4 - u'm 

360° , , 

— 2(Li 4“ O.bloy 4“ Lz) tan • (38) 

This completes the determination of all the e.s.-^ential 
dimensions. 

In all the equations above in which dimensions are 
detei'inined it will be noticed that the thickness and 
density of the laminations cancel out. C'on.>^eciuently, 
the dimen.sions of the laminations depend only on 
the geometry of the lamination and the velocity of 
sound in the lamination material. 


1.3.3. t Tube-and-Plate Transducer 
Elements 


Design of the Mechanic.^l Parts of the Element 
Conventional QC-Like Type. The conventional 
QC'-like transducer consists of a heavy steel dia¬ 
phragm plate which is backed by a large number of 
thin-walled magnetostrictive tubes. The distance be¬ 
tween centers of the tubes .should not be greater than 
one-eighth of a flexural wave length in the diaphragm 
plate at the frequency of operation. If the distance 
between centers is much greater than this, the dia¬ 
phragm will not act as a unit piston but like an arraj' 



sectiorvoi oreo 
density 
sound velocity 


. de*)5Hv; Cj. velocity 


Figure 6.5. Simplified element of a tube-and-plate type 
of transducer. 


of more or less independent small sources which can 
easily get out of phase with each other and cau.se 
pattern trouble. If the thickness of the diaphragm 
plate is less than one-eighth of a compressional wave 
length in the steel, it acts as an almost pure mass 
attached to the magnetostrictive tubes. The node is 
located in the tubes a short distance from the plane 
of attachment to the plate. Figure 65 shows a simpli¬ 
fied form of such a vibrating element. The distance 


CONFIDENTIAL 


















»ESU;\ OF MBRVTIN<; ELEMENTS 


07 


from the free end of the tulie to the node i>s just one- 
fourth wave length in the metal tube. In conventional 
designs, the ma,ss of the short length of tube Li be¬ 
tween the node and the diaphragm mass is usually 
negligible in comparison to the diaphragm mass, and 
consequently it can be considered as a massless 
spring having a sjn-ing constant, 


K = 


A.Eo 

TT’ 


(39) 


where -do is the cross-sectional area of the tube in a 
plane parallel to the diaphragm, and E is Young’s 
modulus. The lowest frequency of re.sonance of such 
a system is therefore. 


fo — 


From this, 


Also, 


1 (4 

I (M 

II 

(40) 

A 2 E 2 

Air'-f q-Mz 

(41) 

X 2 C 2 

' ^ r ^ Vo 



Thus the total length of the tube is 


A2E2 C2 

Aw^f Uh ^ 4fo' 


(42) 


The mechanical Q of a transducer of this ty])e, 
based on the ratio of the mechanical reactance to the 
water radiation resistance (i.e., not considering any 
internal mechanical damping), can be found by de¬ 
termining the effective mass of the vibrating parts, 
multiplying this by the angular frequency and com¬ 
paring the product with the radiation resistance. 
That is. 


Qn. 


2rrfnM* 

•I 3 (p^) water 


(43) 


The effective ma.ss M* is defined in equation (ba). 
The effective mass may be found by determining the 
peak kinetic energy of the actual system and dividing 
it by the sciuare of the rms velocity of the radiating 
face. 

If the rms velocity of the radiating face is denoted 
by Vo, and if the jdate portion of the elementary \-i- 
brator as shown in Figure Go is considered to act as a 
lumped ma.ss, the peak kinetic energy of the lumped 
mass is 4 / 3 ^ 0 “- It can be readily shown that the jjeak 
kinetic energy of the cjuarter-wave portion of the 
tube is ecpial to the mass of one-eighth of a wa\-e 


length of the tube times the square of the rms ve¬ 
locity of the free end of the tube. The velocity of the 
free end of the tube can l)e derived from the condi¬ 
tion that total momentum of the vibrating element 
must be zero. This velocity turns out to be 


where 



mo 


P 2 A 2 C 2 

Stt/o 


(-14) 

(45) 


is the mass of a length of the tube corresponding to 
1 2ir times the wave length. Consequently the kinetic 
energy of the cpiarter-wave portion of the tube is 



(46) 


In practical ca.ses the mass and velocity of the Li 
jjortion of the tube are so small that the re.sulting 



0 2 4 6 8 lO 12 

Mj/mo 


Figure 66. Ratio of M* as calculated by M* = M 3 
(1 -|-43/3 Ormo) compared to the correct value for 
variou.s values of Ms/mc,. 


contribution to the total kinetic energy is negligible 
in comitarison to that of the other parts. Therefore 
the total kinetic energy of the element is veiy nearly 


-j- —WJii 




(47) 


and consecpiently the effective ma.ss is 


M* = 4/3 + 




+ 1 


(48) 


In engineering practice hitherto, the effective ma.ss 
has been calculated on the assumption that the 
kinetic energy of the (juarter-wave portion of the 
tube is equivalent to one-half of its mass vibrating 
with an amplitude which is. 


4/3 44/3 

V 2 = Vo — = Vo - 

TT TTWo 

- nio 


( 49 ) 


COXFIDEXTIAL 





































U8 


THEORY AND DESIGN OE MAGNETOSTRICTION SCANNING SONAR TRANSDUCERS 


This value of Vo is derived from the balance of mo¬ 
mentum when the vibrator is assumed to consist of 
two lumped masses, one of mass and velocity Vn 
and the other of mass (t '4)mo and velocity v^. Actu¬ 
ally this gives too high a value for and conse¬ 
quently gives values of 



which are too high by about 40 to 50 per cent. Fig¬ 
ure 06 shows the ratio of the M* given by this method 
to the correct value, plotted against Mz/iriiy. This 
ratio is 



It has also been considered that the contribution of 
the tube to the effective mass is 2Ms-/m, where m is 
the mass of the entire tube. This makes the total 
effectiv^e mass 

/ 24/.A 

= --)• (52) 

This is a better appro.ximation than that given in 
equation (50), but for practical values of ilfs/wo it 
is still 35 to 45 per cent higher than the correct value. 

A general discussion of the tlieory of a magneto- 
strictive tube free at one end and terminated by a 
lumped mass at the other eml is given in Chapter 3. 
hiquivalent circuit diagrams are shown in Figures 25 
and 27 of Chapter 3. The ratio of the mechanical Q 
to its value Qo when Mz/mi) = 0 is plotted against 
Mz/rtiy^ in Figure 20 of Chapter 3. 

TT (pC) A tube ^ 

C?o = --——— (53) 

2 {pC)u'A f;ice 

For nickel tubes 

„ ,A tube 

Qo = do-- 

- * face 


( W (,)2 

(m„)3 


P2..42C2 P2‘'l2 

27r/o (^^ 0)2 

PzAzCz psA.i 


Stt/o (A’o)3 

(«■„), = 

C 2 

(«. - d*- 

Now con.sider the portion of the tube L^: 

c-i 

d/o’ 

Peak momentum = — (^ 0 ) 2 ^ 2 , 


(5d) 


Lo = 


(55) 


Peak kinetic energy = -(piii) 2 r 2 “. 


In the L\ portion of the tube: 


U 


1 


cot' 


(An) 

urn 

Peak kinetic energy = 


p.'iA 3 
-P 2 A 2 


tan {kojzliz 


=]■ 


Peak momentum = -|-(mii) 2 P 2 [l — eos (A:o) 2 Avi], (56) 


(A'a)2C 


^1 


2 L 

— (sin (A’ii) 2 Ci) (cos (A’o) 2 C 


.)]■ 


In the Lz (jjlate) .section: 

Peak momentum = -(-(w(i) 3 Po-sin {kn)zLz, 
imn)3V»- 


Peak kinetic energy 


2 


{k„)zL 


^3 


(57) 


(sin {k„)zLz){cos (^ 0 ) 3 ^ 3 ) 


The condition that the total momentum be zero gives 
the relation I^etween Vz and Vq: 


Vz {>rh)z sin {k\^)zLz 


(58) 


Vq {itii^z eos {ki))zLji 

The effective mass of the entire .system is the total 
kinetic energy divided by Vq-. This is. 


Sometimes it is desired to tlesign a tul)e-and-plate 
transducer in which the plate thickne.ss is greater 
than X/ 8 . Such a thick jjlate does not act as a lumj^ed 
ma.s.s. The general theorv of tlesign of such elements 
in which the thickne.ss of the plate is ecpial to or less 
than X/4 will now be given. The symbols are as given 
in Figure 65. Also, /o = fretiuency of meclianical 
resonance. 


M* = I {(m„)2 


(wi)) 3 ’ sin’ {kk)zLz 


(^(1)2" COS" {ki^zlji 

{kt))z{Li + Lz) — (sin (A'(i) 2 //i)(cos {k^^zLl) 
d" (wn)3|^(A’ij)3Av3 + (sin (A’n)3T,3)(cos (A:o)3T3)l} ■ (59) 


It is evident from either equation (48) or ecpiation 
(59) that the effective ma.s.s of the .system reduces 


CONFIDENTIAL 
























DESIGN OF VIBRATING ELEMENTS 


419 


rapidly as the ratio of Ms/mn is decreased. If 
can be decreased without decreasing the effective 
radiating area .Is, then the mechanical Q can be de¬ 
creased. However, this decrease in Q automatical!}' 
decreases the efficiency, as may be seen by inspection 
of Figure 27 in C’hapter 3. There it is to be noted that 
if the magnetic flux density (both a-c and d-c) is uni¬ 
form along the entire length of the tube and if all of 
this flux is linked by every turn of the winding, then 
the mechanical impedance seen from the electric side 
of the hypothetical tran.sformer is 






X- 


Lm„ 2Mz . 


(hO) 


times the actual mechanical impedance. (Here X is 
the magnetostriction constant.) At mechanical 
resonance the mechanical branch of the circuit is 
resistive and this i-esistance appears as 


/f/.(elec) 


4ir'\f'N~R i, (median ical) 


d/3 , . mu 

2 


- h 1 H- 

Lm„ 24/3J 



(hi) 


on the electric side. This resistance is in parallel with 
the core resistance Rc and hence competes with it for 
current. As the ])ower dissipated in each of these 
parallel branches is inversely proportional to the re¬ 
sistances, it is desirable that /?/, (electrical) be as 
small as possible in comparison with Rc in order to 
get high electromechanical efficiency. From equa¬ 
tion ( 01 ) it is obvious that the value of /?/, (elec) is 
made smaller by increasing the (d/ 3 / mn) ratio. C’onse- 
quently the efficiency at re.sonance increases with the 
(d/ 3 /wo) ratio until the load resistance Rl (elec) be¬ 
comes smaller than the copper winding resistance. 
The \'alues of d/ 3 /mo used in conventional tube- 
and-plate transducer elements range from about 
4 to 10. 

Magnesium or Plastic Faces. The close tolerances 
on the phases of the elements of a given scanning 
sonar transducer make it desirable to keep the me¬ 
chanical Q of the elements comparatively low .so as to 
allow rea.sonable tolerances on the frequencies of 
resonance of the elements. It has been j^ointed out 
above that the mechanical Q of the tube-and-plate 
tyjDe of elements can be lowered by making the mass 
of the plate portion le.ss without changing the ratio of 
the radiating face area to the cross-sectional area of 
the tube. It has also been pointed out that lowering 
the Q decreases the efficiency at resonance unle.ss 
•something is done to increa.se the effective core re- 


.sistance {Rc as indicated in the equivalent circuit 
.shown in Figure 27 of (diapter 3). 

One way of decreasing the mass of the plate portion 
of the element is to make it thinner. There is a limit 
to thi.s, however, because if the plate is made too thin 
it becomes too flexible and does not act as a rigid 
piston. I'he plate mass may be reduced without ex- 
cessi\’e flexibility if the plate is made of a material 
with low density and reasonably high modulus of 
elasticity. 

Aluminum and its alloys or magnesium and its 
alloys are materials of this type in which the ve¬ 
locities of sound are nearly as great as those in steel 
or nickel but the densities only about one-fourth to 
one-third as great. By the u.se of such materials it is 
possible to make a diaphragm [jlate which has a me¬ 
chanical strength as great as steel but with a mass 
about one-third as great. Some .successful model 
transducers of this type have been designed and con¬ 
structed by Peek of the Bell Telephone Laboratories 
(see Tables 3 and 4 of C'hapter 8 ) which have efficien¬ 
cies of the oi'der of 10 per cent and Q’s of about 10 . 
One of the difficult technical problems encountered 
in the construction of transducer elements of this 
type is the attachment of the tubes to the plate in a 
uniform and satisfactory manner. 

C'ertain of the plastic materials, or laminated ma¬ 
terials impregnated with plastics, can also be used as 
diai)hi-agm plates of low mass. Most of the pure 
plastics have moduli which are too low to be satis¬ 
factory unless the face is made more than a quarter 
wa^■e length thick. Most of the pure i)lastics are too 
compliant to distribute the force fi-om the end of the 
magnetostrictive tube to the broad area of the plate, 
and consequently the plate acts neither as a lumped 
ma.ss nor as a stiff piston. Troul)les due to odd modes 
of \’ibration in the plates usually re.sult. Plates made 
of laminated glass fiber impregnated with bakelite- 
type re.sins have mechanical characteristics that are 
practical for transducer diaphragm plates. Such 
laminated materials are not mechanically isotropic. 
The modulus is greatest in the directions parallel to 
the glass fibers. The technical problem of satisfac¬ 
torily attaching tubes to plates of this kind has not 
yet been solved. One of the best ways is to terminate 
the tube on a small metal button with a good soldered 
joint and then cement the button to the i)lastic with 
.some suitalde cement such as Cycle-Weld. 

Half-Wave Plates with Tubes. A section of a half¬ 
wave plate backed by a half-wave magnetostrictive 
tube is .shown in Figure 67. In this case the particle 


CONFIDENTIAL 











420 


tiif:()rv and desi(;n of >ia(;netostrh:tion scanning sonar transducers 


velocity is the same for all three of the antinodal 
positions. The effective mass of the system is very 
nearly the ma.ss of half the plate portion and the me¬ 
chanical Q’s are approximately 46, 43, 15, ami 10 for 
plates of nickel, steel, aluminum, and magnesium 
respectively. This particular design gives a very low 
efficiency because the electromechanical coupling is 
so small. The coupling can be impro\'ed by increasing 
the length of the plate to slightly over a half wave 
length and decreasing the length of the magneto- 
.strictive tube until it approaches a length .somewhat 
greater than a quarter wave length. This brings the 


NOOC 


I 

I NODE 



M*» Y [(*o), ♦ (mjj] ' 


Pi C, *,♦ Pi Cj Aj 


46 if foce bloch IS of niciiet 

43 M M " •• ste«l 

15 II H « <« M olufmnum 

10 *t II II “ "'ognesium 

Figure 67. Half-wave, tube-and-plate oscillator. 

node near the jtoint of attachment of the tube to the 
plate, allows the velocity of the free end of the tube 
to increase to a value much greater than Cn, and con¬ 
sequently increases the strain in the nickel for a given 
Vn of the front face. However, this increases the me¬ 
chanical Q of the .system considerably. For the same 
mechanical Q, this type of element is less efficient 
than the conventional QC type. 

In a half-wave plate type of tran.sducer. which 
consists of a large number of tubes mounted on the 
.same plate, troulile is u.siially caused by mechanical 
coupling due to the Pois.son effect in the region of the 
node. This effect can be minimized by cutting notches 
between the portions of the jdate that belong to the 
imlividual tubes. If a metallic bridge connecting the 
various blocks is ilesired, it should be located near 
the top or bottom surfaces away fi'om the nodal 
region to prevent the type of coupling just mentioned. 
In any type of tube-and-plate construction it is good 
practice to have only one node in the vibrating sy.s- 
tem, and this node .should lie located a short distance 




up the tubes from the jilate so that a minimum 
amount of mechanical coupling is produced. 

Wedgr-T^pc Plate. An example of the weilge- 
type jilate is shown in Figure 25. There are few ad¬ 
vantages in this type of element. Howe\'er, sufficient 
information will be given to aid in the design of such 
an element and to help understand its mechanical 
characteristics. 


Area Velocity 

Active Face 



Figure 68 . Fundamental section of a tube-and-plate 
type element in which the plate portion is wedge 
shaiied. 


A section of an element of this type is shown in 
Figure 68. The jilate portion may be consitlereil as a 
long, narrow jirism, the active face of which is about 
one-half wave length witle and 5 to 7 wave lengths 
long (these wave lengths are for water at the fre- 
cpiency of re.sonance), and the tubes or their equiva¬ 
lent exteml out from the narrow face of the prism. 
The areas indicated refer to the cross-sectional areas 
corresponding to a unit height of the prism and the.se 
areas lie in planes perpendicular to the direction of 
the strain or particle velocity. 

The ratio of the jiarticle velocities at Ai and Aq is 

Cl _ A^i(A’a'o) • ./Q(A’.ri) — Ji{kxo) ■ Noikxi) O'O') 

i’u A'lf/r.rn) • Jn{k.Vo) — ./i(A’.ro) ■ A^o(A'.ro) 


CtdXFIDEXTIAL 








































DESIGN OF VIBRATING ELEMENTS 


421 



Figure 69. Comparison of a standard tuhe-and-plate element with two kinds of wedge-and-tiibe elements. In each 
ca.se .4tube = 0.114 cm*, Tface = 1.82 cm*, frequency = 14.87 kc. 


where the ./’s and N’s are the Bessel and Neumann 
functions of the orders indicated by the subscripts. 
The condition for resonance in the first mode of vi¬ 
bration is 


pi-d (iVn~ -Ni(A~oXo)e/o(/;:oX) ./i(knXo)A^o(knX) "1" 

J'o *'■^1 L.Vi(A'o.ro)./o(A''oa’o) — Ji(A'().rn).Vo(A'o3‘o) J 

xdx, (6()) 


./i(A-Xi)Ni(Ajo) - Ni(A-Ji)./i(Axo) ^ poCoAo 

Jo(A'Xi)*Vi(A'Xo) — iVo(Axi)./i(A'j-o) piCiAi 

tan k'L , ((>3) 

where A’ = 27r//ci and A' = 2irf/c2. The freciuency 
of re.sonance will be designated by /o and the corre- 
sjtonding k’s by ko’s. 

The ratio of the particle velocity at the free end of 
the tube to that at the active face is 


1^0 


Vl 

Vo 


sec ko'L • 


(b4) 


The kinetic energy of the tube part of the system is 


P2.42t’2‘r^ 

2 


—' sin 2A,j'L 
2 A"o 


(bo) 


and that of the wedge part is 


where x is the distance measured outward from the 
virtual vertex of the wedge, ('onsecjuently the effec¬ 
tive mass of the system is 







sec-A'o'L 


+ 


Pi-lo /^■'orNi(A’o2'o)'/o(A’ox) Ji(kt)Xo)Noikox) ”1" 

X(] LNi(A'(i.rQ)iAo(A(>ro) “ •/i(A'oXo)iVo(AoXo) J 


xdz- (b7) 


Just as for all the other types, the mechanical Q is 
gi\'en Iw 

2TrfoM* 

'4o(pC)ur 

The equivalent circuit .shown in Figure 27 of Chap¬ 
ter 3 may be applied to this type of tran.sducer ele- 


C(3NFIDENTIAL 












































































122 


TIIEOKV AND DESIGN OE MAliNETOSTKIGTION SCANNING; SONAR TRANSDUCIEKS 


meiit by taking; Ri, = Ao{pc)„.(vn/vi)-, Mi ociual to 
the second term of e(]uation ((>7), multiplied l)y 
ivn/vi)~, Li (mechanical inductance) equal to the first 
term of equation ((>7), and making- the transforma¬ 
tion ratio 


1 _ -i-ir-fd-N- 

('hfh')" ^'(l ~ k'L)- 


(b8) 


"fcj give the readei' a concrete idea of the velocity 
distributions, eciuivalent masses, mechanical Q’s, 
etc., of the wedge-and-tube type element as com¬ 
pared to the conventional tube-and-plate type, three 


T.\Br.E 2. 



Tube and 
plate 

Tube and 
long 
wedge 

Tube and 
short 
wedge 

Actual nias.s of plate 
or wedge (gms) 

27.0 

59.7 

42.5 

?«n (grams/radian) 

.5.20 

5.20 

5.20 

M/mo 

5.20 



M* (effective mass, gms) 

137 

837 

,567 

Qm 

49 

298 

198 

Rl/Rc 

0.76 

0.16 

0.22 

Maximum efficiency 

0.57 

0.85 

0.82 


.specific cases have been analyzed (piantitatively: 
(1) the standaril (^GA Type 941, 14.87 kc; (2) a long 
wedge having the .same face area, nickel tube ai’C'a, 
and frecpiency as the (^G.V; (3) a short wedge ha\'ing 
the same face area, nickel tube area, and fretiuency 
as the QGA. 


In Figure (>9, a compai'ison is made between the 
standard tub(‘ and ])late of the QGA Type 941 pro¬ 
jector, with resonant freciuency of 14.9 kc and two 
tube-driven w('dges. The elements are drawn to 
scale, and it is assumed in each ca.se that the .slotted 
tid)es are made of annealed nickel, with a ().U25-in. 
wall. The plate and wedges are of steel. The wind¬ 
ings are as.sumed to e.xtend along 4 cm of the tube 
nearest the node, so that this length ol tube con¬ 
tributes to the core impedance, ('omputed values of 
.significant charac'teristics of the three elements are 
given in Table 2. The.se computations are ba.sed on 
the following \'alues: 

/o = 14.9 kc, 

A-'.v, = 0.193, 

A steel = 0.187, 

R, = 1.9 X lO^iVGihms (A" = turns of windings). 
A'r = 1.85 X 10“-*A"-ohms, 

Pr = 30, aiul 

Resistivity = 8 X 10“^ ohm cm. 

Eddy currents are a.s.sumed the same as tor fiat 
lamina and resistance of windings is negligible. 

It is to be noted that the high efficiencies for the 
wedges as computed for the ideal conditions as.sumed 
are obtained at the price of values of Q which are 
prohibitively high for scanning sonar use. Moreover, 
efficiencies that could be obtained in any actual case 
would be much lower than tho.se shown because ol 
the copixu- lo.sses in the windings and internal me¬ 
chanical resistance, both of which were neglected in 
the com]xttation for Table 2. 


COXFIDEXTIAL 










Chapter 14 

CONSTKUCTION AND TESTING OF SCANNING TRANSDUCERS 


n.l INTRODUCTION 

The preceding chapter presented tlesigns for sev¬ 
eral fundamentally different types of transducers 
that might be successfully used in scanning a sound 
field. Each type possesses its own peculiar set of 
l)roblems and advantages. This di.scussion will he 
limited to an a.ssembly of laminated stacks arranged 
so that the active faces form a cylinder. Practical 
methods of consti’uction and precautions for main¬ 
taining tolerances will be described. The testing pi-o- 
gram, both before and after assembly, will be given 
in detail. A brief outline of the experience gained in 
building and testing .several models is also included. 

14.2 MANUFACTIRE OF LAMINATED 
STACKS 

There was considerable variety in the tyj^es of 
laminated stacks built by Harvard Underwater 
Sound Laboratory [HUSL]. They ranged in size 
from the large 8^ X 8M X 3^-in. block of lamina¬ 
tions down to the 13-4 X ^ X %6-in. .stack u.sed 
as one element in an array. This chapter, however, 
will be limited largely to tho.se u.sed in the scanning- 
sonar and related projects. In general, they are illu.s- 
ti-ated by the two stacks shown in Figure 1. One of 
the.se has a slot completely across the magnetic cir¬ 
cuit into which a permanent magnet is inserted for 
polarization. The other must be ijolarized lyv sending- 
direct current through its windings. In every case 
they ha\’e been built up of thin nickel laminations 
with a bonding cement to assure permanent form 
and rigidity. They ai'e provided with windings, end 
caps for mounting, and some means of polarization. 
This .section will deal with the details of this process 
and the means of determining how succe.ssfully it 
has been done. 

11.2.1 Problems Involved in 
Construction 

There are a number of problems involved in the 
manufacture of laminated stacks. The bond between 


laminations must give the stack strength to with¬ 
stand the handling of winding- and mounting. In its 
mounted position the stack will not ordinarily be 
subjected to tension or compre.ssion, but it will have 
to stand the shear and l)ending stre.ss of accidental 
blows. Since the binding material may strongly in¬ 
fluence the characteristics of the stack, choice of 
binding material is also limited by factors other than 
strength. 



Figure 1. Scanning sonar stacks. 


^^'here a number of stacks are assembled into one 
unit to give a composite pattern, the.se stacks must 
be quite uniform in freiiuency and amplitude. The 
methods of stack manufacture used must re.sult in 
stacks that are close duplicates of one another. Rapid 
and accurate methods of testing frequency and ampli¬ 
tude should be available. To avoid the introduction 
of phase differences, careful alignment of the lamina- 


423 


CONFIDENTIAL 












421 


CONSTRUCTION AND TESTINC; OF SCANNING TRANSDUCERS 


tions in the stack and installation of the stack in the 
mounting are also necessary. 

In a complete .scanning sonar transducer there may 
he from 40,000-80,000 laminations. The handling of 
such a ciuantity of fragile parts pre.sents a difficult 
problem to the manufacturer. After being launched, 
the laminations must be carefidly cleaned, annealed, 
and given a coat of con.solidating cement. If the nec¬ 
essary tolerances are to b(' maintained in matching 
.stacks, the laminations must be handled in such a 
way as to avoid deformation of any kind. These 
laminations may be made into as many as 192 stacks, 
each of which must be ecpiipped with winding caps, 
end jdates, a rubber diaphragm, and a coil on each of 
the two winding cores. To turn this amount of de¬ 
tailed work into an acceptable manufacturing j^rocess 
is a problem rivaling that of the original design. 


11.2.2 Preparation of Laminations 

Before going into a detailed description of the man¬ 
ufacturing methods in use at present, it would be 
well to i)oint out a few precautions. However rugged 
a laminated stack may be in aiipearance, it is really 
a delicate temperamental instrument in behavior, 
prone to spurious modes of ^’ibration and high in¬ 
ternal mechanical lo.sses when pooi'ly constructed. A 
good design can easily be lost through poor execu¬ 
tion. Alethods of handling laminations have de¬ 
veloped gradually under stress of growing demand. 
Inve.stigation of i:)roblems has gone along with pro¬ 
duction, and usually the aim of an investigation has 
been to find something that would do rather than to 
discovei’ the best j^ossible method. Therefore, the 
following de.scription presents a tec'hnique that has 
been found to work in i)ractice but does not repre.sent 
the best development po.ssible. 

A good die for cutting the laminations is e.ssential. 
The laminations should be consolidated into stacks 
under pre.ssure. Stacks more than 4 in. high should 
be consolidated in sections. If stacks are highei' than 
this, it is difficult to hold the laminations in jumper 
alignment and to develop a j)ressure evenly dis¬ 
tributed through the stack. The bonding cement 
should be thermosetting rather than thermoplastic. 

baminations that have been battered and bent by 
careless handling cannot be consolidated into stacks 
that meet the recjuired dimensional tolerances; they 
are likely to stack higher on one end or on one side 
than on the other. C'rimps and kinks may peianit 
strains to be relieved in undesiietl directions. A cer¬ 


tain amount of cold-working results from mistreat¬ 
ment after annealing. To avoid deformation, lamina¬ 
tions should be racked up as they come from the 
punch press. Figure 2 shows a satisfactoiy rack and 
tray for this purpo.se that also permits the storage of 
large (piantities in a small space. 



Figure 2. Rack for laminations .as they come from the 
jiunch pres.s. 


The metal strij) from which the laminations are 
jjunched comes coated with an oil film which, along 
with other dirt, must be removcal before annealing. 
Nickel laminations which show the slightest oil stain 
beforehand will .show, after annealing in air, a gray- 
green .scale ciuite loosely attached to the metal sur¬ 
face. The aijjiearance of scale has at times been 
ascribed to other cau.ses, but it .seems reasonably 
certain that a clean lamination will never show the 
effect. 

For cleaning, the racks of closely jiacked lamina¬ 
tions are placed in a tray containing enough ethylene 
trichloride to cover them. The solvent penetrates 
rapidly into the capillary spaces between laminations 
and in a short while the oil has tlififused throughout 
the .solvent. The rack of laminations is then placed 
in a tray of clean .solvent, where the oil again becomes 
diluted. Four .such treatments, with a 4-hr .soaking 
for each, produce clean laminations. This method 
requires a little time, but it involves no handling of 
the lamination and practically no labor. 


CONFIDENTIAL 












MAMFACTURE OF LAMINATED STACvS 


425 


Nickel is usually annealed at 930 to 1000 C in air. 
The thin oxide coating so produced has excellent 
insulating properties, and no other insulation is 
needed if during the annealing the laminations are 
so spaced that oxj’gcn is available to give a uniform 
coat over the entire surface. An annealing rack of 
stainless steel is shown in Figure 3. Clean laminations 
may be loaded rai)idly onto the.se racks with mini¬ 
mum handling. One method uses a 3^in. brass tube 

APPROXIMATELY 90 NOTCHES 
PER BAR, 900 ODD IN ALL 



that has one end fashioned to slide along the top of 
the rack. This tube carries the laminations to be 
racked, and they are fed off into the .slots as the rod 
slides along the top of the rack. This scheme, of 
course, can be used only with the slotted type of 
lamination, but .some similar scheme will serve for 
other types. The laminations may also be speedily 
removed by reT'ersing the loading proceiss. 

U.2..4 Consolidation 

The choice of a bonding material for consolidation, 
the method of applying it, and the pres.sure used 
during curing depend upon the amount of mechanical 
strength that can be sacrificed for uniformity and 
efficiency. It has been repeatedly demonstrated that 
too strong a bond between laminations is a .source of 
trouble. Stacks so built .show unwanted re.sonances 
near the main resonance frequency, a wide variation 
in resonance frequency, and a low potential effi¬ 
ciency. The minor resonances of a 25-kc stack will 
disappear if the stack height is cut down to 1 in. or 
less for stacks of higher frequency. Increasing the 
thickness of the bonding layer will yield a stronger 
stack but may result in lower efficiency."® 


Methods of Applying C'e.ment 

Three different methods of applying the bonding 
cement and consolidating the stack have been suc- 
ce.ssfully u.sed in the laboratory. One method takes 
advantage of cajiillarity in the thin spaces between 
laminations. The correct number of laminations are 
jilaced in the stacking jig and put under slight pres¬ 
.sure. The outside aligning pins are withdrawn from 
the jig and a medium coat of (’ycle-Weld P-55-() 
cement is brushed on the outside .surface of the .stack. 
The cement is rapidly absorbed into the spaces be¬ 
tween laminations. The stack should be given a 
30-min. air dry, and a 30-min. oven dry at 180 F. 
The aligning pins are then replaced and the lamina¬ 
tions put under a pres.snre of 50 to 100 lb per .s(j in., 
depending on the amount of burr and lamination 
thickness. The cement cures in about 15 min. after 
the stack has reached a temperature of 300 F. This 
procedure results in stacks that are uniform in fre¬ 
quency behavior and of high potential efficiency but 
moderate strength. If stacks of greater strength are 
desired, this method may be modified. The cement is 
brushed on in consifleralde quantities and given an 
8- or 10-hr cure at 2()0 F. The longer curing period 
allows the solvent to escape before the bond is com¬ 
pletely established. 

In a .second method of con.solidation, the lamina¬ 
tions are placed fiat on wire mesh and sprayed with 
C'ycle-Weld C-3 cement. After a 5-min. air dry, they 
are turned oT-er and sjTrayed on the reverse side. An 
air dry of 20 min. is followed by an oven dry at 180 F 
of about 20 min. The laminations are put in a jig 
under a ]5ressure of about 200 to 300 lb per sq in. and 
given a 20-min. cure at 320 F. It is important that 
the actual temperature of the stack be 320 F. The 
coat of cement may be built up to any desired thick¬ 
ness by repeated spraying; great strength can be at¬ 
tained in this way. C’oats of 0.0015-0.002 in. are 
sufficient for maximum strength, but, for stacks used 
in .scanning sonar transducers, coats thicker than 
0.0005 in. are not desirable. 

Cements like Cycle-Weld P-55-() that flow when 
heated are likely to bond over the whole surface. 
Such bonds are usually strong enough to introduce 
parasitic resonances. C’ycle-Weld C’-3 is a nonflowing 
cement and, when aj)plied in thin coats, bonds the 
lamination only liy a narrow strip around its edge. 
Stacks thus consolidated very .seldom show unde¬ 
sired resonances. 

The bakelite resins are excellent if strength of bond 
is the prime requisite. It is also likely that proper 


CONFIDENTIAL 







426 


CONSTHICTION AM) TKSTIM; OF SCANMM; TK ANSDl CERS 



USE OF TOP PLATE TO EXERT PRESSURE USE OF PLUNGER TO EXERT PRESSURE 

Fi(!ure4. a. Stacking jig, original model. H. Stacking jig, improved model. 


solvents ooukl be found to permit their application 
by any of the methods recommended here. 

The cement may also be api)lied by dipping. C'lose 
control of the time of withdrawal of the lamination 
from the cement must be maintained to avoid the 
formation of a bead on the end. Dipjting has two ad¬ 
vantages: a more uniform coat is jto.ssible and le.ss 
handling is necessary than with spraying. The lami¬ 
nations are hung on hooks and lowered into a vat of 
the cement. A mechanical device for withdrawing 
them at a uniform I'ate of speed is easily ari'anged. 
The speed of withdrawal depends upon the viscosity 


of the cement used, ^^’ith C’ycle-Weld C’-3, of specific 
gravity U.92, this .speed is about 9 in. per minute. 
Rapid evaporation of solvent from the dipping vat 
reciuires frequent checks on the density of the cement 
and the addition of solvent. The same drying and 
curing ])rocedure is u.sed as with spraying. The suc- 
ce.ss of this process depends upon having laminations 
free of burrs, excellent consolidating jigs, and close 
control on the cement. It has been used to i)roduce 
uniform .stacks of good strength with Cycle-Weld 
spiTyv-tyjTe C’-3 as the cement. Cycle-Weld P-55-() 
may also be used, but it must be thinned to a specific 



CONFIDENTIAL 





























































































































































MANUFACTURE OF LAMINATED STACKS 


127 


gravity ot about 0.8() and the laminations consoli¬ 
dated with pressures of 30 to 50 lb per sq in. 

Consolidating Jigs 

A good jig is an essential feature of a successful 
consolidating technique. A .shrinkage in height u.'^u- 
ally occurs during the curing jirocess, necessitating 
the use of calibrated springs to in.sure a constant 
])re.ssure as the stack shrinks. Aligning jiins must be 
carefully spaced to maintain close tolerances on stack 
dimensions. As the jiressure is applied, the lamina¬ 
tions should slide freely along the pins to produce 
uniform jires-siire throughout the length of the stack. 
This applies also to top and bottom plates of the jig 
of Figure 4A. The .slightest mi.salignment of the plate 
at either end ot the stack would make it lodge on one 
or moi-e of the pins, thus reducing the jiressure on the 
stack. The improved jig shown in 4B prevents this. 
A piston .slightly smaller than the laminations, fitting 
loosely between the pins, applies the pre.ssure through 
a ball-and-socket joint. 

Heat Treatment and Recovery of Poor Stacks 

Experiment has shown that the characteristics of 
a stack will be slightly changed if it is heated to a 
temperature higher than that at which it was con¬ 
solidated. If it is not rai.sed above this temperature, 
further heating for short periods does not .seem to 
affect it. If a rubber diaiihragm is to be attached by 
heating, the consolidated stack should be rai.sed to 
the temperature required for attaching the rubber 
before mea.surements are made on it. In general, one 
may safely a.ssume that a jioor stack is the result of 
too strong a bond between laminations. This bond 
may be weakened by raising the temperature of the 
.stack to the point of decomposition of the cement. 
The resulting stack will have little mechanical 
strength, but, if it is a sjilit stack and was produced 
by brushing cement onto the outside surface, it may 
be strengthened by brushing cement onto the inside 
surface and curing a .second time. 

11 . 2 . t Testing Equipment and 
Preliminary Testing 

Stacks used as elements in an assembly must meet 
certain reciuirements with regard to potential effi¬ 
ciency and resonance frequency. A standard jiro- 
cedure for detei'inining these characteristics has been 
to make impedance measurements at a sufficiently 
large number of frequencies, in both air and water, 
to determine the motional impedance circles. This 


was so long a task in the ca.se of a 192-stack a.s.sembly 
that it was nece.ssary to devise quick and easy sub¬ 
stitutes for the.se measurements. The impedometer, 
the conductometer, and the vector impedance locus 
plotter were developed for this purpo.se. Descriptions 
of these dei'ices are gii’en in CJiapter 9. 

To use the impedometer, the stack to be measured 
is connected in the circuit of Figure 5.\ as element T. 


R| 




B 


Figure 5. Circuit of impedometer. B. Impedance 
diagram. 

The switch K is thrown to and the outiiut of the 
oscillator is regulated until the voltmeter reads 
J?s/10", where n is a small integer. The switch K is 
thrown to T, making the voltmeter read iZrl/lO". 
The oscillator frequency is then varied through the 
range of the impedance circle. Figure 5B .shows the 
position of the vectors for which magnitudes are 
read from the voltmeter. The maximum impedance 
on the circle ma}" be averaged with the minimunx 
imjiedance on the circle Z^in to give the average im¬ 
pedance Zavg. The average frequency/a vg is obtained 


CONFIDENTIAL 

















128 


( ONSTUUCTION AND TKSTINA; OK SCANNING TRANSDUCERS 


by varying the oscillator freciuency between/,„ax ivnd 
/min until the ^’oltmeter indicates the \'ahie of the 
average impedance. An imijedance measurement 
taken several kilocycles away from the i-esonance 
frequency is quite useful for comparing the extent of 
magnetic polarization and the core impedance with 
those of other stacks. 

\\’hile the impedometer measures magnitudes of 
the impedance ^■ectors only, experience has shown 
that stacks uniform with respect to these cjuantities 
and without any minor resonances within the main 
impedance circle will work together .satisfactorily. 
The pre.sence of minor resonances is indicated by ir¬ 
regular \'ariations in the impedance readings taken 
through the frequency range. The ratio of Z,nax to 
Z,nin gives an a])proximate value of the tliameter of 
the impedance circle and, therefore, of the potential 
efficiency. The mean frequency, fr, is ordinarily 
quite clo.se to the resonance frequency and can be 
used in freciuency-matching of the stacks. The 
method is fast; scarcely more than 1 min. per stack 
is necessary to obtain and recoicl all the data. 

A preliminary test with the impetlometer may be 
made before winding to avoid the expen.se of winding 
a stack that may later l:>e di.scarded. A coil of the 
kind to be used in the transducer may be preformed 
slightly oversize so that it will slip down into place 
around the winding core. A magnet, used at the 
strength that it maintains in air, is jiut into the mag¬ 
net slot. Thus ecpiipped, the .stack can be te.sted for 
the j)resence of minor re.sonances, and a good value 
of the ratio of Z„,,,x to Z„,i„ can thus be obtained. 
Accurate frequency measurements cannot be made 
under the.se conditions since the stack will be under- 
jjolarized and there will be considerable flux leakage 
due to the loose windings. 

11.2.5 Winding 

Before the final tests can be made for the selection 
of stacks to go into an as.sembly, the stacks must be 
wound, and this winding must thereafter remain per¬ 
manently fixed in jjosition. To prepare a stack for 
winding, a collar of insulating material is put around 
each leg. It has been found convenient to use a band 
of Jfg-in. air-cell neoj^rene which is slightly wider 
than the length of the coil and fits .snugly on the core. 
This band shoidd be cemented to the core in two 
jdaces to prevent .slipping. The air-cell neoprene 
affords e.xcellent mechanical insulation and will fur¬ 
nish the pres.sure release nece.s.sarv if the stack is to 
be mounted in oil. 



Figure 6. .Aluminum end cap; end cap under wind¬ 
ing. B. Bakelite end cap; end caji over winding. 


Two types of end caps, shown in Figure (>, have 
been used for stack mounting in scanning sonar 
transducers. Figure 6A shows an aluminum-cast end 
cap which is attached before winding. Xe-in- thick¬ 
ness of corprene or air-cell neoprene isolates the end 
cap from the stack. Since the end caps hold the stacks 
in operating positions that are quite critical with 


CONFIDENTIAL 





























MANUFACTURE OF LAMINATED STACKS 


429 


respect to spacing, close tolerances must be main¬ 
tained in placing the end cap on the stack. Vulcalock 
cement serv'es very well to attach these parts, but 
care must be taken to avoid an excess that will run 
over into the magnet slot. If the end cap of Figure (iA 
is u.sed, it is attached first and the insulating band 
and windings are i)ut on over it. The bakelite 
mokh'd end cap of Figure ()B is attachetl after the 
winding is done. 

The presence of the magnet slot and the fact that 
few turns of wii-e are used make it jjracticable to wind 
the.se stacks by hand. A winding jig of the t.ype 

NEOPRENE GLUED TO 



shown in Figure 7 is convenient for this purpose. It 
should be remembered that these stacks are made of 
soft annealed nickel and that dropping them, letting 
them fall over, or clamping them in a vise is to be 
carefully avoided. To minimize mechanical losses, 
the windmgs must fit loosely. The u.se of 0.010-in. 
removable spacers at each end of the stack during 
winding makes it possible to i)ut on a neat, well- 
placed winding that will not bintl the stack after the 
spacers are withdrawn. Because of the flux leakage 
acro.ss the winding slot, the placing of the winding is 
critical. The position of the winding relative to the 
motion made by the stack affects the jjotential effi¬ 
ciency and the resonance frequency. Therefore, the 
winding must be firmly attached to prevent slipping. 
This can be effectively done after winding by briush- 
ing on a heavy coat of thermosetting cement to hold 
the winding to the rubber band beneath it. 

11.2.6 Selection of Stacks 

At the time of this writing no .satisfactory method 
for testing stacks after attaching the rubber dia¬ 


phragm had been developed. Im{)edance mea.sure- 
ments in air with the diaphragm attached do not 
show the beha\'ior of an unloaded stack and are not 
indicative of the stack’s behavior in water. Imped¬ 
ance measurements in water are not a .sufficientl.y 
.sensitive means of detecting frequency variations 
between stacks. It was necessary therefore to u.se, as 
a basis of selection, the data taken on the stacks be¬ 
fore the rubber diaphragm was attached, on the 
assumption that the process of cementing rul)ber to 
the stack never re.sults in a ladical change in its be¬ 
havior. Since there is considerable evidence that this 
a.ssumi)tion is unsafe, it should be investigated 
further. 

The best jn-ocedure develojjed at HUSL is the 
l)asing of stack .selection on conductometer measure¬ 
ments made after the stack has had its final winding 
and is polarized as it will be in the final a.s.sembly. 
A descrijition of this step is gi\ en in the next section. 
The conductometer measures the maximum con¬ 
ductance and, as shown by the admittance circle, the 
frecpiency of maximum conductance, which is cjuite 
close to the frequency of maximum efficiency. 

11.2.7 Polarization of Stacks 

The last step in the a.s.sembly of a stack is to pro¬ 
vide it with a permanent magnet. A de.scription of 
the magnet to be used and its characteristics have 
been given in Section 13.3.3. The magnet ma.y be a 
single block or several blocks cemented together and 
shaped to fit the slot precisely. This must present a 
clean smooth surface free of any material that might 
cement the magnet to the stack. The magnet is kept 
in place, without binding, by the coil and the end caps. 
In some cases the oi)en end of the magnet slot has 
been clo.sed by nonmagnetic metal strips, isolated 
from the stack with air-cell neoprene and attached 
by screws to the end caps. In others the slot was 
clo.sed temporarily by paper tape and permanently 
by the final mounting base. Early experiments 
showed that cementing the magnets into the slots 
.seriously affects the behavior of the stack. 

With the magnet in position, the stack is placed in 
a magnetic field of sufficient strength to saturate it. 
The stacks are to be mounted with like poles adja¬ 
cent; therefore, the direction of magnetization and 
the polarity of the winding terminals must be re¬ 
corded. Experience has shown that after magnetiza¬ 
tion there may be considerable variation from stack 
to stack in the core impedance and the impedance 


CONFIDENTIAL 





CONSTRUCTION ANT) TESTINT; OF SCANNINC; TRANSDUCERS 


4;{(> 


at resonance. This is partially due to lack of uni¬ 
formity in the magnets and to variation in the in¬ 
cremental permeability of the stacks. This .situation 
may he improved lyy a slight demagnetization. 

The practice was to bring the impedance of all 
stacks that go into the same a.s.sembly to the same 
magnitude at a freciuency about 10 kc away from 
resonance. The reason for this operation may be 
readily understood by referring to the two imi)edance 
circles of Figure 8. The two cur\’es show the relati\-e 



Eigure 8. Dependence of impedance curve on mag¬ 
netization. 


t'alues of imjjetlance of two stacks jtolai'ized to differ¬ 
ent degrees. The freciuencyon the dotted curve is 
the same as the freciuency/c' of the solid line, and if 
the impedance of the two stacks can be made to 
match at this frequency, the two imitedance curves 
will practically coincide — an essential requirement 
if the two stacks are to vibrate in jihase when driven 
from a common source. If the stack represented by 
the dashed line is depolarized slightly, its impedance 
at fc will move up the arrow to the impedance at f/. 
The freciuency/c is chosen some distance from reso¬ 
nance, since at such a point frequency settings are 
not socritical and the impedance becomes truly repre¬ 
sentative of the core impedance. 

Demagnetization is easily effected by sending bO- 
cj’cle current through the windings of the stack. The 


circuit of Figure 9 provides a cpiick and ea.sy scheme. 
On the right of the diagram is the impedometer and 
on the left is a ^dlriac transformer; T is the stack, 
.4 an a-c ammeter, R> a rc'sistor to protect the am- 



osc 


VARIAC 

t'lGURE 9. Circuit for adjusting magnetization. 

meter, and K a multiple .switch. \4'hen K is thrown 
to the right, the \'ariac is connected to the stack, and 
the oscillator ami voltmeter are across the standard 
resistor /?«. In this position, the o.scillator is set at the 
frequency at which the impedance of the .stack is to 
be stabilized, and the output of the o.scillator is set to 
make the voltmeter read imi)cdance directly. From 
the \’ariac, a .surge of a-c current is .sent through the 
windings of the stack. Then switch K is thrown to the 
left, taking the ^'al•iac out of the circuit and i^utting 
the voltmeter and oscillator acro.ss the stack. The 
re.sulting impedance of the stack can be read directly 
fi’om the voltmeter. Getting the desired impedance 
is nece.ssarily a trial-and-error proce.ss, but it is 
greatly facilitated by this ea.sy switching circuit. If 
one o\'er.shoots the mark, the stack must be rejjolar- 
ized and the demagnetization repeated. It is to be 
noted that stacks who.se impedances are higher when 
.saturated than the impedance cho.sen for polarization 
cannot be used in the a.ssembly. 

u.-i PREPARATION OF THE TRANS¬ 
DUCER ELEMENT 

General Design 

One element of a .scanning transducer may consist 
of a single stack or of two or more stacks operating in 
series, parallel, or in series-parallel combination. 
Where a thin rubber diaphragm is cemented to the 


CONFIDENTIAL 
































PREPARATION OF THE TRANSDUCER ELEMENT 


131 


/l6 CELL-TITE NEOPRENE 


I'B CELL-TITE NEOPRENE 


RUBBER FACE 


CYCLE-WELD 
BONDS 




ACTIVE FACE 
BAKELITE 
END CAPS 

WINDINGS 
50 TURNS 
*^9 ENAMELED 
WIRE 


LEAD WIRES 


TIE ROD 

.036 
STAINLESS- 
STEEL CAN 


RUBBERSEAL 
COMPOUND “2 


**I9 SOLID ENAMELED 
WIRE 

BAKELITE PLUG 


STAINLESS- 
‘ STEEL CAN 


ATOMIC HYDROGEN 
WELDED CORNERS 


OZZLE FOR LEAD WIRES 


Figure 10. Component parts of IIP-2 clement. 


radiating faces nf the stacks, this diapliragm may he 
continuous for the full length of the element. This 
assembly is further strengthened by a thin aluminum 
spline fastened to the back of each stack. A preferred 
way of building uj) the element is to jtrovide each 
stack with a separate diaphragm and mounting. A 
brief description of the various methods used at 
HUSL follows. 

The first of the IIP series of .scanning transducers 
was like that .shown in Figure 15 of C'hajiter 13, ex¬ 
cept that it was not enclo.sed in a rubber lioot. The 
windings, winding slots, and stack face were in dii-ect 
contact with water. Each element consisted of one 
12-in. stack wountl with a wire who.se insulation was 
suppo.sedly water-resistant. Two defects in the opera¬ 
tion of the tran.sducer called for a change in element 
design. The bare metal face of the laminated stack 
was quite erratic in its contact with the water and 
the wire insulation would not stand up under oper¬ 
ating conditions. The.se difficulties were .solved by the 
rubber jacket .shown in Figure 15 of Chapter 13. 


1 1.3.2 Elements Housed as Indi¬ 
vidual Units 

The .second transducer of the HI’ .series, the HP-2 
(Figure 19 of C'hapter 13), was so de.signed that each 
element, consisting of a .single 18-in. .stack, was 
housed in a .stainle.s.s-steel container made watertight 
by a seal for the conductors and a rubber strip ce¬ 
mented to the container and to the active face of the 
stack. The component parts of such an element are 
shown in Figure 10 and the a.s.sembled tran.sducer in 
Figure 11. 

In this design, the fatal defect, the inherent weak- 
ne.ss of the bond between the rubber diaphragm and 
the stainle.ss-steel container, has already been indi¬ 
cated in Chapter 13. The difficulty is twofold. The 
first is the fact that a bond between stainle.ss steel and 
rubber using the u.sual techniipies has proved in¬ 
herently weak. The second is the difficulty of apply¬ 
ing and maintaining the necessaiy pre.s.sure.s simul¬ 
taneously to the face of the stack and to the edge of 


CONFIDENTIAL 





















CONSTRUCTION AND TESTING OF SCANNINi; TRANSDUCERS 


U2 


the stainless-steel housing. After -se\’eral months of 
experimentation, a 3()-element unit was produced 
wliich was sufficiently watertight for a trial at New 
London hut which developed leaks after a very short 
period of u.se. 



Figure 11. HP-2 traasducer. 


The most effective means found of securing a Iiond 
between the rubber diaphragm and the stainle.ss steel 
was to etch the steel with concentrated hydrochloric 
acid. The outside lii).s of the container were coated 
with jjetroleum jelly, and the container was im¬ 
mersed to a depth of in. for 5 min. in the acid bath, 
giving an etched inner surface to which the rubber 
would adhere. Various other methods of mechanically 
roughening the surface of the stainless steel, such as 
sanding or filing, were tried but acid-etching proved 
the simplest and most effective. 

\'arious methods of jiroducing the requisite pre.s- 


sures between diaijhragm and stack and diaphragm 
and housing are shown in Figure 12. Of the.se meth¬ 
ods, that shown in Figure 121) pro\-ed the simj^lest 
for securing a reliable bond between the molded 
rublier face and the stainless .steel. The following de¬ 
tailed de.scrijition of the jirocedure is given to illu.s- 
ti-ate the general method of Cycle-Welding rubber to 
metal, a proce.ss that was used in all subseipient 
scanning sonar transducers built at HLT^SL. 

The I'ubber face is first “cyclized.” Those portions 
of the rubber that are not to be treated are coated 
with petroleum jelly, and the face is immersed for 
5 min. in concentrated .sulphuric acid. This produces 
a haitl siu'face layer, which then is thoroughly broken 
up by Iiending and stretching the rubber. Cycle- 
Weld 55-0 is then brushed onto the cyclizetl surface 
and allowed to dry for at least 12 hr. To speed up 
the operation, the brushed surface may be allowed to 
air dry for 3U min. and then placed in an o\’en for an 
eipial time at a temperature of 180 F. 

A heavy metal jig is used for cementing the ruliber 
to the stack face. The particular form of jig used de- 
jiends upon the contours to which the rubber is to be 
cemented. That for the HP-2 elements is shown in 
Figure 12. The as.sembled unit is jilaced in the jig and 
the rubber face fitted into po.sition, with the expo.sed 
rubber surface dusted with talcum and covered with 
thin paper to prevent the rubber from sticking to the 
liressure ])late of the jig. The closely fitting wood 
strip (12D) is laid on the rubber face and the cover 
plate is screwed into position. A thei’mocouple is 
placi'd between the rubber face and the wood strip 
so that the face temperature can be measured. 

Six or eight of the assembled jigs, each with an air 
jjressure line attached, are placed in a thermostati¬ 
cally controlled oven. An air pressure of 45 lb per 
SCI in. is applied to give the needed pressure between 
the I'uliber and the sides of the container, and the 
oven is heated to a temperature (usually 350 F) that 
will yield a stack temperature of 300 F. This condi¬ 
tion of temperature and pre.ssure is maintained for a 
])eriod of 20 min. 

The [irocedure just described was the most in¬ 
volved of any of the Cycle-Welding processes used in 
the production of scanning sonar tran.sducers. It was 
complicated by the nece.ssity of applying vertical and 
lateral ijressures simultaneously during the curing of 
the Cycle-Weld. 

The other methods that were tried are indicated in 
Figure 12. That indicated in 12C was fairly succe.s.s- 
ful. The inner tubes of 12B were apt to blow out. 


CONFIDENTIAL 











PKEPAKATION OF THE TRANSDUCER ELEMENT 






H€ot Res(Stont 
Rubber inner Tube 


To Source of Controlled 
Air Pressure 


Rubber Face being 
Cycle-Welded info Ploce 


CYCLE-WELDING of FACES in CANS. 

MECHANICAL PRESS METHOD 


CYCLE-WELDING of FACES m CANS, 

RUBBER INNER TUBE METHOD 



To Source of Controlled 
Air Pressure 


Rubber Face being 
Cycle-Welded into Ploce 


Heot Resistant 
Rubber Oiophrogm 


CYCLE-WELDING of RUBBER FACES, 

RUBBER PRESSURE DIAPHRAGM METHOD 



CYCLE-WELDING of RUBBER FACES, 

DIRECT AIR PRESSURE ON SPECIAL FACES 


Figure 12. Jigs for Cycle-Weldiiig IIP-2 element. 


CONFIDENTIAL 




































































































































































t:u 


CONSTKl ( TION AM) TESTIN); OF SCANMNt; TKANSDlCEKS 


Many elements were “eannetl” l)y one or other of the 
methods deserihed. Some of them showed appai’ently 
perfect adhesion of the rubber to the stainless steel 
after a period of more than 18 months. Nevertheless, 
the uncertainty of a permanent lx)nd with C'yele- 
^^'eld thermosetting resin makes this method one 
that cannot be recommended, much as sejjarately 
housed elements are to be desired. 

Elements Housed in a 
Rubber Boot 

The magnetostrictive elements of HP-2 weie .sal¬ 
vaged and incorporated in the form shown in Fig¬ 
ure 15 of C'hapter 13. designated as HP-2B. d'hey 
were mounted on a cylindrical spool and the whole 
as.sembly enclosed in a molded rubber boot 3^ in. 
thick. To secure acoustic contact between the ele¬ 
ments and tlie water, the entire transducer was e\'ac- 
uated and filled with outga.s.sed castor oil, using the 
method and apj)aratus shown later in Figure 20. This 
transducer pro\ed .seaworthy and was installed on 
the F’SS Cythera, where it served a useful purpose in 
the scanning sonar experimental jjrogram. All subse¬ 
quent models were housed in the same general fash¬ 
ion, differing only in details of the means of securing 
acoustic contact with the water. 

11.3.1 Transducers witb PM 
Polarization 

The elements of the transducers described in the 
preceding sections each comprised a single continu¬ 
ous stack of laminations held in ])lace by tie rods 
pa.ssing through the entire length of the stacks and 
attached to the flanges of the .sujiporting .spool In' 
.screws engaging the end caps. All were polarized by 
a d-c component of the current through the windings. 

This construction was not j)ossit)le with elements 
polarized by sintered-oxide magnets. The sintered 
oxide itself is fragile, and since it is carried loo.sely in 
.slots in the laminations, the u.se of elements con.sist- 
ing of two or more short stacks is definitely indicated. 
The HP-3 transducer is typical and its a.s.sembly will 
be given in detail. Each element contains four wound 
stacks, each with a sintered-oxide magnet and end 
caps. The steps in the assembh' of the four stacks 
into an element are clearly indicated in Figure 13. 

The rubber face strip is cyclized and coatetl with 
55-G Cycle-Weld. The fronts of the stacks are also 


given a coat of the same material and both are al¬ 
lowed to dry. 

The sintered-oxide magnet plates are removed 
from the stacks, each one marked with the .serial 
number of the stack from which it was taken. The 
four stacks are fitted together as shown at B of Fig¬ 
ure 13, a tie frame made of two plates and two tie 
rods being used to hold them in place while the rub¬ 
ber face is fitted into po.sition. The element is then 
placed face down in the curing jig as shown at C. The 
asseml)ly frame is remo\'ed and replaced by another 
adjusted to hold the element to its proper length. 
The top ])late of the jig is screwed down, compre.ssing 
the spi'ings to gi\’e the desired pressure of 45 lb per 
scj in. A thermocouple is placed at the center of the 
element near the face. The curing process is the same 
as that described in the ca.se of the H1’-2B. 


Figure 13. Illustration of HP-3 element assembly. 

Aftei' the element has cooled, the magnets are re- 
jilaced, each in its proper stack. The element is 
.strengthened by a thin .strip of aluminum faced with 
3d^6-in. air-cell neoprene fastened to the back by 
screws which pass into the end caijs. The magnets are 
repolarized in place in the .stacks, by placing the ele¬ 
ment in the field of a powerful electromagnet. 

This procedure completes the assembly of the ele¬ 
ment except for electric connection of the elements 
and adjiLstment of the magnetization. 

li t ASSEMBLY OF A TRANSDl CER 

11.1.1 Selection of Elements 

Indi\'idual elements in the cylindrical array are 
.selected and arranged with a view to obtaining the 
minimum difference in resonant frequency between 
adjacent elements. The procedure followed in the 
case of the HP-3 is illustrative of the method fol- 




CONFIDEXTIAL 






ASSEMBLY OF V TKWSDUCEK 


t33 


lowed generally in hnilding scanning sonar trans¬ 
ducers. 

The freciuencies of maximum conductance of the 
individual stacks of each element were averag(‘d. 
The elements were then chosen in the order of these 
averages. They were arranged in the transducer so 
that the elements with the lowest and highest aver¬ 
aged freciuencies were diametrically opposite, with 
the intervening elements placed in the order of their 
a\-eraged fretpiencies, as shown in hdgure 14. The 
outer number identifies the selected stack and the 
inner one gT’es the deviation in its measured fre- 
cpiency from 27,000 c. 



F'icjvre 14. Stack arraiiKcment of 48-elemeiit trans¬ 
ducer. 


This method of arranging the elements leaves 
something to be desired, since it is ciuite probable 
that handling of the individual stacks in assembling 
them into elements may materially change their 
resonant freciuencies. Precise determination of the 
freciuency of maximum conductance of the a.ssembled 
elements would furnish a better criterion for arrang¬ 
ing them in the assembled transducer. This wovdd, 
howec'er, involve another set of measurements and 
it is doubtful whether the possible improvement in 
receiA'ing pattern that might result wordd warrant 
the expenditure of time reciuired to make them. 

Elements were so oriented that the magnetic polar¬ 
ities of the sintered-oxide plates were opposed in ad¬ 
jacent elements, a North pole being jilaced next to 
another North, and so on. 


T.\bi.e 1. Data of Figure 14*. 


Posi¬ 

tion 

Stave 

no. 

Segment 
no. 1 
freq. 

Segment 
no. 2 
freq. 

Segment 
no. 3 
freq. 

Segment 
no. 4 
freq. 

.Average 

freq. 

1 

A10 

741 

456 

458 

731 

-66 



— 00 

-95 

— 45 

-70 


2 

A19 

767 

492 

522 

751 

-42 



-60 

-60 

-35 

—15 


3 

.\57 

773 

332 

.5.34 

771 

-40 



-40 

-20 

-.50 

-30 


4 

.\37 

807 

552 

.528 

799 

-36 



-55 

-20 

-2.5 

—45 


o 

A9 

763 

470 

472 

689 

-.32 



— 3o 

-30 

-40 

-25 


6 

.A21 

727 

518 

504 

769 

-1.3 



-10 

0 

0 

-40 


7 

.454 

855 

538 

546 

841 

2 



—15 

5 

20 

-20 


8 

A23 

725 

524 

410 

779 

24 



20 

25 

25 

25 


9 

A18 

663 

494 

498 

655 

32 



35 

30 

40 

25 


10 

A20 

703 

516 

490 

69.3 

44 



fiO 

.35 

30 

50 


39 

A29 

709 

512 

484 

787 

37 



35 

15 

65 

35 


40 

A42 

.305 

582 

126 

299 

31 



10 

50 

40 

2.5 


41 

A52 

671 

530 

536 

599 

21 



15 

10 

2.5 

3.5 


42 

Ao 

587 

462 

468 

591 

12 



0 

25 

2.5 

0 


43 

.455 

717 

228 

324 

765 

— 5 



-10 

—15 

0 

5 


44 

.459 

691 

482 

526 

729 

-2.5 



-.30 

-35 

— 5 

-30 


4.5 

A38 

825 

564 

94 

859 

-.3.5 



-.50 

— 45 

—15 

-30 


46 

.46 

291 

2.30 

3.54 

297 

-.36 



—55 

-30 

-30 

-30 


47 

.422 

707 

486 

488 

747 

-41 



-30 

-35 

-65 

-35 


48 

.44 

555 

406 

464 

753 

— 54 



-40 

-80 

— 55 

-40 



*If oompletp data are d.-sired see reference 56. 


11.1.2 Assembly on the Spool 

The spool for the HP-3 is shown in Figure 15. An 
annular disk is welded in.side the spool 4 in. from the 
i)ottom end. The disk is u.sed for the cable water .seal 
into the junction I)ox at the lower end of the trans¬ 
ducer. The bottom end of the sja^ol contains the 
water seals for the sets of three wires which lead to 
each of the elements. The top end is machined to take 
a standard QC’ Hange for support of the transducer. 

The cylindrical jiortion of the spool is covered with 


CONFIDENTIAL 



























4S6 


CONSTKUCrnON AND TESTING OF SCANNINIi TK VNSDUCERS 


a piece of 3^-in. corprene and a piece of 3^-in. C’ell- 
Tite neoprene cemented into place with \'ulcalock. 
The corprene jn-ovide.s a firm backing for tlie elements 
and the neoprene is sufficiently soft so that the ele¬ 
ments can be fitted accurately into place. Rings of 
3/^-in. corprene were cemented to the inner faces of 
the s)30ol ends. 



Holes for the element-retaining .screws were drilled 
into the toji and bottom ends of the spool while they 
were being machined. A piece of steel straj) was cut 
•so that it fitted into the S))ool in place of an element. 
This strap was drilled carefully to match the holes 
in the ends of the spool so that the strap could be 
used as a templet in drilling the holes in the emls of 
the element .supports. After being drilled and counter¬ 
sunk, the elements were pre.ssed into place and the 
leads drawn through the holes in the bottom plate. 
The retaining .screws were then ])ut in and the ele¬ 
ment fastened. Pieces of jd^g-in. corprene were placed 
between the elements to cushion them and i^rovide 
pressure-release material should it become neces.sary 
to fill the tran.sducers with ca.stor oil. 

The three leads for each element were brought into 
the junction box space at the bottom of the tran.s- 


ducer through molded rubber pieces. Sealing was 
accomplished by screwing a hollow i)lug down on top 
of the rubber pieces. This expanded the rubber and 
sealed the hole from the element chamber to the 
junction box. This method of .sealing was not very 
satisfactory. There was a strong tendency for the 
rubber ])iece.s to twist as the .seals were screwed into 
place, causing a short circuit in the element chamber. 
In the HP-2, the water seals were forced into j^lace 
by machine screws and there was no tendency for the 
lead wires to twist. The use of this type of pres.s-in 
seal, when po.ssiljle, is recommended instead of the 
.screw-in seals. 



Figure 16. HP-3 transducer lieforc aiiplication of 
rubber boot. 

The diameter of the rubber boot foi- the HP-3 was 
12 per cent smaller than the outside diameter of the 
element circle. Both the faces of the elements and the 
inside of the boot were given repeated coats of castor 


CONFIDENTIAL 



































































ASSEMBLY OF A TRANSDUCER 


137 


oil beginning several days before the boot was to be 
applied. Finall}' one end of the boot was clamped to 
a circular piece of iron strai) and stretched to a di¬ 
ameter greater than that of the element circle. After 
a rush coat of castor oil, the boot was pulled down 
over the transducer. Figure 1(5 shows the assembled 
transducer ready for the application of the boot. 


c 


A 



preferable to any of the commercial de\'ices tried, 
particularly those in which the fastening was accom- 
pli.shed by making a punch mark in the buckle to 
hold the strap. Punch locking failed repeatedly and 
was definitely unsatisfactory. 

Another tyj)e of clamping band illustrated in Fig¬ 
ure 17B offers the advantage that it can be tightened 
from time to time. It is not entirely e\'ident that this 
is necessary, however. Its greatest disadvantage is 
that the buckles are large and project so far beyond 
the body of the transducer that there is danger of 
ilisplacing the straps in handling. 

11.1.3 Cable Connections 

The cable for the HP-3 reciuired 147 conductors. 
Commercial cable was not immediately available and 
resort to a homemade cable was necessary. Forty- 
nine trijjlets were twisted first, from which seven 



The methods of clamping the rubber to the end 
plates are shown in Figure 17. In the first method, 
shown in A, a stainless-steel strap wrapj^ed twice 
around the tran.sducer was threaded through two 
buckles, one of which was free to slide along the 
sti'aj). A number of methods were tried for tightening 
the strap. A simple screw clamp was finally devised 
with which the strap could be j:)ulled against the end 
buckle, ^^dlen adequate tension was .secured, the 
clamp was folded away from the transducer and the 
straj) snubbed over the buckle. The free end was then 
tucked through the .sliding buckle, which was tapped 
into i)lace next to the end buckle. The excess strap 
was then removed. This method of fastening proved 


strands containing .seven trij)let.s each were made. 
The seven strands were then twisted into a single 
cable. 

The making of multistrand cables in lengths of 
50 ft or less for e.xperimental and emergency use 
proved (juite feasible. When two or more wires are 
twisted together, each wire must be free to twist on 
its own axis. The simple device for permitting this is 
shown in Figure 18. The ball bearings permit the 
wire to twist freely even when under considerable 
ten.sion. The ])rocedure for making the 147-conductor 
cable was as follows. 

Three wires of equal lengths were fastened in the 
hooks projecting from the bearing plate, passed 


CONFIDENTIAL 











































CONSTRUCTION AND TESTING OF SCANNING TRANSDUCERS 


i:{8 


through holes in the following plate, and the free ends 
fastened to a hook in an ordinaiy hand drill. As the 
hand drill was operated, the following plate was car¬ 
ried back towai’d the bearing plate. The tightness of 
twist was controlled by adjusting the rate of move¬ 
ment of the bearing plate to the rate of twisting. 
Care was taken to see that the untwisted wires be¬ 
tween the two plates were free to turn each about its 
own axis during the twisting. After .seven triplets had 
been twisted, they were attached to the bearing plate 
and twisted in the opposite direction to the twist 
gi\'en the triplets. The cable was completed by twist- 



Figure 19. Water seal of cable to junction box. 


ing the seven strands together, again reversing the 
direction of twist .so that the final direction was the 
same as the original twist given the triplets. The 
assembled cable was so heaxy that several jieople 
were required to -support it to maintain a reasonably 
uniform tension in the seven strands during the final 
twisting, which had to be done by hand by the person 
working next to the follower plate. When completed, 
it was bound with adhesive tape at intervals of 3 ft 
and encased in fabi'ic-coated fire hose. 

All the triplets in any one strand were color-coded 
so that any triplet could be -selected and any wire of 
that triplet identified- All seven strands were identi¬ 
cal in color codes but a string tracer was twisted in 
one of the strands. In the completed cable this strand 
was one of the outside six. It was thus po.ssible to -se¬ 
lect aiy strand, any triplet, and any wire at any 
point in the cable. 

The water .seal admitting the cable to the trans¬ 
ducer junction box is shown in Figure 19. Each con¬ 
ductor was pa.s.sed through a hole in a bakelite plate. 
This plate was held by screws in a potlike container 
which was heated and filled with Rubberseal com¬ 
pound No. 2. This container was then screwed into 



Figure 20. .\ppanitus for ca.stor-oil filling. 


place on the annular plate inside the spool cylinder. 
A rubber ring gasket between the container and the 
ring completed the water .sealing of the tran.sducer 
junction box. 

it.l.t Filling with Castor Oil 

The technique of filling a tran.sducer with castor 
oil is well illustrated in the a.s.sembly of the HP-3S 
t ransducer. 


C’ONFIDEXTIAL 

















testing; scanning tkansducers 


139 


At first it was believed necessary to fill this trans¬ 
ducer with castor oil, since its conical shape might 
cause poor acoustic contact between the rubber boot 
and the faces of the elements. The procedure followed 
will .serve to demonstrate the precautions that 



Figure 21. Schematic of oil-filling apparatu.s. 


should be taken in ca.ses where oil filling is necessary. 

The apparatus is shown in Figure 20 and illustrated 
schematically in Figure 21. An annular plate of metal 
rested on the gaskets at the top of the transducer. In 
the top of the plate was a groove for another gasket, 
on which rested a thick disk of plate gla.ss. Two jiieces 
of pipe were screwed in the ring. One of these was 
used for exhausting the entire transducer by means 
of a Megavac pump. The other was u.sed for admit¬ 
ting castor oil. During the filling process all water 
seals were left open except one, which was used for 


making the connection to the oil lead. The tran.sducer 
was tipped slightly so that this seal was lower than 
the others to prevent entrapment of air relea.sed in 
the last stages of the process. Procedure was as 
follows. 

1. The entire apparatus, including the transducer, 
was evacuated to a pressure of 1 mm of mercury or 
less. 

2. Heating current was applied to the coil of re¬ 
sistance wire on the column. The temperature of the 
column was raised to approximately 50 C. 

3. The oil lead to the transducer was closed and 
the hose to the oil reservoir was opened slightly .so 
that oil entered the top of the column slowly. A great 
amount of gas dissolved in the oil came out as it en¬ 
tered the top of the column. The rate of admission 
of oil was determined mostly by the amount of 
foaming. The oil de.scended the column over a loo.se 
packing of stirrup-shaped pieces cut from rubber 
tubing. 

4. When the pres.sure flask below the column was 
filled, the pinchcock between it and the column was 
clo.sed. The vacuum lead to the flask was then closed 
and the oil lead to the tran.sducer opened. Air was 
then admitted to the top of the flask and the oil en¬ 
tered the tran.sducer jjartl.y by gravity but mostlj' by 
atmospheric pressure. 

5. When the flask was nearly empty, the oil lead 
to the transducer was clo.sed and the flask was evacu¬ 
ated and reopened to the column. A large transducer 
such as this reciuires .several gallons of oil and about 
3 hours to fill. 

6. When oil appeared in all water-seal holes, the 
process was stopped and air admitted to the trans¬ 
ducer. This had to be done slowly with an extra sup¬ 
ply of outgas.sed oil on hand, since as the air entered 
the boot expanded, calling for an additional quantity 
of oil. It was neces.sary during this last stage to be 
able to see what was going on in.side the tran.sducer, 
hence the gla.s.s plate. 

14.5 TESTING SCANNING 

TRANSDUCERS 

11.5.1 Purpose 

The complete study of the behavior of a multiele¬ 
ment transducer calls for a large number of acoustical 
measurements on the completed instrument. Such a 
study is desirable on tran.sducers of this type during 
the experimental stage. Although a small number of 


CONFIDENTIAL 









































CONSTRUCTION AND TKSTING OF SCANNING TKANSDUCKKS 


tto 


response and pattern measurements will serve to 
show whether the o\’erall performance is as exj)ected, 
an extensive program of tests covering the full i-ange 
of ojjerational recpiirements is needed to detect and 
diagnose minor failures and to supply information for 
possible imjjrovement. 

1 1.5.2 Tests of HP-3 No. 1 

.\s an illustration of these tests, measurements 
made on the HP-3 No. 1 will be pre.sented with an 
analysis of their significance. The HP-3 No. 1 is a 
48-element tran.sducer resonating at 2(1.2 kc. Each 
element is comjiosed of four stacks so connected that 
the two center stacks may be used alone for a bi-oad 
vertical beam (called the 0:1:1:0 connection) or the 
two center stacks may be used in series with the out¬ 
side stacks in parallel (called the 1:2:2:1 connection) 
to give amplitude .shading. 



Figure 22. Receiving pattern of .single element of 
HP-3 in horizontal plane. 


Tests with Transducer Mounted \'ertically, 
Measurements with 0:1:1 :0 

The receiving responses of all 48 elements were 
taken. The frequencies of maximum respon.se ranged 
from25.8 to2().2. The width of the response peak 3 db 
below the maximum was (with a single exception) 
between 2.9 and 3.4 kc. The Q’s lay between 7.4 and 
9.0, with an aveiage of 8. (One element showed a 
Q of 12.4, indicating poor acou.stic contact with the 
rubber boot.) The open circuit sensitivities ranged 
from —91.1 to —89.1 db, with an average of about 
— 90.1 db vs 1 volt per dyne per .sq cm. 

A .sample receiving pattern of a single element in 


Table 2. IIP-3 No. 1 Transducer with a 0:1;1:0* 
Connection. 


Element 

Res. 

f requency 

Width 
3-dh down 

Q- 

Sensitivity 

1 

26 kc 

3.2 kc 

8.1 

-89.6 

2 

25.8 

3.3 

7.8 

-89.5 

3 

26 

3.2 

8.1 

-90.4 

4 

26.1 

3.4 

7.65 

-90.7 

5 

26 

3 

8.7 

-89.6 

6 

26 

3.3 

7.9 

-89.4 

7 

26 

2.9 

9 

-90.4 

8 

26 

2.9 

9 

-90.1 

9 

26 

3.4 

7.65 

-90.7 

10 

26 

3.3 

7.9 

-89.6 

39 

26 

3.4 

7.65 

-89.8 

40 

26 

3.2 

8.1 

-90.6 

41 

26 

3.3 

7.9 

-90.7 

42 

26 

3.4 

7.65 

-89.8 

43 

26 

3.2 

8.1 

-90.6 

44 

26 

3.3 

7.9 

-90 

45 

26 

3.5 

7.4 

-89.8 

46 

26 

3 

8.7 

-90 

47 

26 

3.2 

8.1 

-89.3 

48 

26 

2.9 

9 

-89.2 


*If complete data are desired, see reference 5H. 



Figure 23. Pressure and pha-se differences at different 
elements of HP-3 transducer, referred to values at 
element on which incidence of iilane wave was normal 
to the surface. 

the horizontal plane is shown in Figure 22. All the 
patterns taken were nearly identical with this one. 

The results of the phase-pattern measurements 
and jiressure-pattern measurements are given in 
Pdgure 23. The agreement between the pressure pat¬ 
tern of a single element of Figure 22 and the pressures 


C(4NFIDENTIAL 




























































TESTING SCANNING TRANSDUCERS 


III 


shown in Figure 23 is within the experimental error 
of the measurements. Tlie phase j)attern is about 
normal. The observed phase differences between ele¬ 
ments are about 1 to 2 per cent higher than tho.se 
jn-edicted l\v a.ssuming that the path differences are 
l^roportional to 1 minus the cosine of the angle of 
incidence and that the velocity of sound is 57,000 in. 
per sec. 


The pattern at 20 kc .show's a \’ariation of ± 1 db, that 
at 24 kc ±2 db, and that at 28 kc +2 db. The pat¬ 
tern at 20 kc is quite .satisfactory, while those at 
24 kc and 28 kc are only fair. 

Admittance measurements were made with the 
transducer in water at the Charles River barge. The 
values of the admittance components for single ele¬ 
ments at 20 kc and 20 kc are shown in Figures 20 


Table 3. Pres.sure pattern measureiuetit.s on HP-3 No. 1 Traasducer mea.sured at 26 kc, sound .source 16.3 ft distant. 
(The 0;1:1:0 connection.) 


.Acoustic axis 
centered on 
elements 

Branch 

Relative Klenieiit Number 

• 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

48-1 

R 

0 

0.1 

-0.6 

-1.0 

-0.6 

-2.5 

-4.3 

-4.3 

-7.0 

-7.2 


L 

0 

0.1 

—0.5 

-0.9 

-1.9 

-3.3 

-4.0 

-6.3 

-7.4 

-7.8 

18-19 

R 

0 

-0.3 

1.1 

0.5 

-1 

-0.8 

-2.8 

— 3.5 

-4.9 

-5.9 


L 

0.0 

0.1 

-2 

0 

-1 

-1.2 

-3.3 

-3.8 

-5.4 

-6.8 

32-33 

R 

0.2 

0.5 

0 

-0.7 

1 

CO 

-2.3 

-3.2 

—5.1 

-6.4 

-6.7 


L 

0 

-0.5 

1 

-0.5 

-1 

-2.2 

-3 

— 5 

-5.2 

-7 

Sum 


0.2 

0 

+ 1.2 

-2.6 

-7.8 

-12.3 

-20.6 

-28.0 

-36.3 

-41.4 

.Average 


-1-0.06 

0 

+0.2 

-0.43 

-1.3 

-2.05 

-3.4 

— 4.65 

-6.05 

-6.9 


Table 4. Pha.se pattern measurements on HP-3 No. 1 Transducer measured at 26 kc, sound source 16.3 ft distant. 
.\11 readings corrected for sphericity of wave front. (The 0:1:1 ;0 connection.) 


.Acou.stic axis 
centered on 
elements 

Branch 

Relative Element Number 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

48-1 

R 

2 

21 

66 

150 

220 

342 

487 

623 

791 

956 


L 

0 

29 

87 

173 

259 

379 

525 

673 

841 

1012 

18-19 

R 

0 

17 

72 

148 

216.5 

342.5 

482 

620 

790 

966 


L 

0 

27 

93 

181 

279 

398 

.548 

678 

869 

1044 

32-33 

R 

0 

28 

86 

172 

258 

383.5 

.528 

679 

844 

1021 


L 

0 

19.5 

72 

146 

226 

354 

496 

638 

817 

981 

Sum 


2 

141.5 

476 

970 

14.58.5 

2199 

3066 

3911 

49.52 

5980 

■Average 


0.3 

24.5 

88 

1.58 

265 

366 

.510 

6.53 

826 

996 

Theor. value 












(1 — cos 8) 

1 

3 

27.8 

77 

149 

244 

360 

494 

644 

809 

984 


360 R,. „ o T- • ^ i. o 1 57.000 o i-r • 

-(1 — cos d)\ R — 8.7.0 in.: X at 26.2 kc = - = 2.17 m. 

X 26.22 


The open-circuit frequency respon.se of all the ele¬ 
ments in parallel is shown in Figure 24. During this 
mea.surement there was an unusually high noise level 
due to electric pickup. How'ever, the portions of the 
response near the frequencies of re.sonance rose well 
above the noise background. The sensitivity at 26 kc 
is about —112 db and that at 52.5 kc is about 
—123 db referred to 1 volt per dyne per sq cm. The 
Q's for the 26-kc and the 52.5-kc resonances are 9.3 
and 33 respectively. 

The patterns at 24, 26, and 28 kc with all the ele¬ 
ments connected in parallel are .shown in Figure 25. 


and 27. The conductances and .susceptances are 
plotted against the element numbers in Figure 26 
and the same values are showm in Figure 27 with the 
R’s (siLsceptances) plotted against the (?’s (conduct¬ 
ances). The latter diagram shows that at 26 kc the 
admittance angles varied over a range of 6.5 degrees 
and the admittances had a variation of ± 5 per cent. 
These variations are somewhat greater than desired, 
but .satisfactory performance of the transducer in a 
trial installation has shown that tolerances as great 
as the.se are allowable. 

The transmitting response at 16.3 ft wdth all the 


CONFIDENTIAL 










































442 


CONSTRUCTION AND TESTING OF SCANNING TRANSDUCERS 



K) 18 26 3< 42 50 58 66 

FREQUENCY IN KC 


Figure 24. Receiving response of HP-3 Xo. 1, all 
elements in parallel. 



Figure 25. Horizontal pattern-s of HP-3 Xo. 1, all 
elements in parallel. 


</> 

o 

1 

2 

z 

CD 

O 

z 

< 

o 


20|-- 


B AT 20 KC 

aI A 










r 1 

/ ' V 

xivrAt— 

B AT 26 KC 



1 

! 


r, ^ 


1 1 1 

G AT 26 KC 


6- 

r 

'VNntTv 

G AT 20 KC 




1 

i 

i 

n_ 





Figure 26. .\dmittance of single elements of HP-3 
Xo. 1 at 20 kc and 26 kc, plotted against element 
numbers. 



Figure 27. Spread in admittances of single elements 
of HP-3 Xo. 1 at 20 kc and 26 kc. 


elements connected in parallel and driven at a con¬ 
stant voltage of 1 volt is shown in Figure 28. The 
peak responses under these conditions are 52 dh at 
20.4 kc and 44.5 db vs I dyne per scj cm at 52.3 kc. 
The Q’s for these resonances are appro.ximately 10 
and 22.7 respective!}'. 


Tests with the Transducer Mounted Horizon¬ 
tally, WITH 0:1:1:0 Connection 

Vertical receiving patterns for single elements at 
2() kc, 24 kc, and 28 kc are shown in Figures 29A, 
B, and C respectively. These patterns are about as 
they .should be according to theory. 


CONFIDENTIAL 


























































































































TESTING SCANNING TRANSDUCERS 


u:\ 


The patterns at 26 kc, with all elements connected 
in parallel, are shown in Figure 30. The side lobes on 
these patterns are higher than predicted by the the¬ 
ory for a line source. This shows clearly that the side 
lobes are higher for a large cylindrical source than 
they are for a line source of the .same length. 

Directivity Index and Efficiency 

From receiving and transmitting respon.se data, 
the measured impedance, and a knowledge of the 
directivity index, estimates of the efficiency of the 
tran.sducer may be made. A single element may be 
regarded as a rectangular source whose length is large 
compared with the wave length of the radiated .sound. 
The directivity index D may be iletermined by the 
method given in Chapter 5 (see Figure 29 of Chap- 



Figure 28. Transmitting response of HP-2 No. 1, all 
elements in parallel. 




Figure 29. Vertical patterns of two single elements at 24, 26, and 28 kc. 


CONFIDENTIAL 











































































CONSTRUCTION AND TESTING OF SCANNING TRANSDUCERS 


m 


ter 5). At 20 kc, the effective radiating widtii w of a 
single element as indicated by the horizontal pattern 
(Figure 22) is 3.8 cm, and the effective length as given 
by the main lobe width of the vertical iiattern is 
22 cm. The wave length at 20 kc is 5.5 cm. From this, 
27rw^ X = 4.3 and / X = 4.1. From the graph of Fig¬ 
ure 29 of C'hapter 5, l/XD = 0.092, D = 0.023, and 
10 log D = -10.4. 

To calculate the efficiency from ecpiation (25a) of 
Chapter 1, the following values are u.sed. 

Sensitivity = — 90 db ref. 1 volt hlyne/cm- 

Zi = 29 + j53, I Z i = 00.4 ohm.s. 

Eff (decibels) = —90 — 20 log 5.5 — 10.4 — 

10 log 29 -h 127 
= - 8.8 db = 0.13. 

The efficiency from the transmitting response is 
computed from equation (20) of C’hapter 1, using 
the following values for the mea.sured quantities: 

)• = 4.90 meters; 

20 log p' = 41.5; 

E = I volt; 

20 log I Zj I = 35.0; 

10 log D = — 10.4; 

10 log Ri = 14.0 

Eff (decibels) = 14 + 41.5 + 35.2 - 10.4 - 
14.0 - 70.9 
= -10.8 db = 0.084 

From similar data for the transducer with all 48 
elements connected in parallel, an efficiency of 0.18 
was computed from the sensitivity and 0.11 from the 
transmitting response. 

In addition to these tests, receiving patterns were 
taken through the lag line and commutator of the 
C’R scanning sonar to show how the transducer 
would actually operate in scanning sonar u.se. Such a 
pattern is .shown in Figure 31. 

14.6 SCANNING TRANSDUCERS BUILT 
AT HUSL 

11.6.1 Early Models 

While the technicpies just described were being de¬ 
veloped, the HP series of scanning transducers was 
being built. The HP-1 and HP-2 are de.scribed in 
Scanning Sonar. The HP-3 has just been de.scribed 
in illustrating the testing and as.sembly procedures.®* 
There remain for brief treatment the HP-3 and 
HP-3DS modifications.®*“ 


11.6.2 HP-3S 

The HP-3S was built for use with a pro-submarine 
.system. It differs from the HP-3 piimarily in that the 
elements are mountetl on a portion of a cone having 
a vertex angle of 12 degrees. This feature was de¬ 
signed to compensate in part at least for the refrac- 
ti\'e effect of temperature gradient, which on the 
aA’ei’age tends to bend the sound pattern downward. 



Figure .30. V'erticiU receiving pattern, all elements in 
parallel at 26 kc with 0:1;1:0 connection of .stacks in 
elements. 

The general jdan of the HP-3S is shown in Fig¬ 
ure 32. The spool was made in three pieces; the base, 
the cone, and the top. The base and the cone were 
welded together. The toj) was screwed to the upiter 
end of the cone with a copper gasket well cemented 
with gasket-cementing compound between the two 
jjarts. After the top had been attached, it was not 
again removed. 

As in the HP-3, the top and bottom flanges were 
slotted to provide attachment for the elements. Each 
element consisted of four stacks identical with those 
used in the HP-3 excejit that, being connected in 
series, only two leads were nece.s.sary for each ele¬ 
ment. These leads were brought out through rubber- 
stem water .seals similar to those previously used. 


CONFIDENTIAL 


















SCANNINC; TRANSDUCERS BUILT AT IIUSL 


445 



Figure 31. Receiving pattern of 48-element scanning 
sonar transducer at 25.6 kc through commutator lag 
lines. 

The HP-3S wa.s desiigned to be mounted on the 
forward deck of a .submarine. When .so mounted, the 
cable would be brought in from the bottom. For test¬ 
ing purposes, a 50-pair telephone cable in a rubber 
.sheath armored with woven wire was used. 

The rubber boot to cover the tran.sducer was 
molded on a specially constructed mandrel. The in- 
.side surface of the boot was repeatedly jiainted with 
castor oil over a period of .several days. The faces of 
the elements were coated in the .same way. The boot 
was then lowered into place and fastened with the 
.same type of bands as were on the HP-3. 

The completed tran.sducer wa.s shown in Figure 9 
of Chapter 13 with the ba.sket or “Turk’.s-head” 
woven fi’om stainless steel wire covering the exposed 
surface of the rubber boot. This was held at top and 
bottom liy two rings, each with 71 projecting pins 
over which the meshes of the basket were hooked. 
The lower ring was drawn down by means of screws 
into the lower Hange, thus causing the basket to grip 
the rubber over the entire surface and insuring inti¬ 
mate contact between the rubber and the element 
faces. The device .serves the further purpo.se of pre- 
A'enting flapping and loo.sening of the boot under the 
impact of the waves when the submarine is operating 
on the surface. The re.search program at HUSL was 
terminated before full-scale tests were made on this 
tran.sducer. 



Figure 32. Section of the HP-3S tran.sducer. 


11.6.3 HP-3DS 

After it had been demonstrated that horizontal 
CR scanning sonar was a feasible underwater de¬ 
tection .system, the idea of applying the same .sort of 
system to the vertical plane was considered for use 
in detecting deep targets. In this system a sound 
pulse was to be sent out mainly in the vertical plane 
in the front two (juadrants and the lower back quad¬ 
rant, followed by reception with a sharp receiving 
beam of sensitivity (10 degrees wide at — G db), 
scanning in the vertical plane at approximately 
30 rps. The beam was split for BDI to aid in training 
the main beam in the horizontal plane. 

It was planned to mount the transducer on a 
standard vertical training shaft for azimuth training. 
The acti\'e elements extending over three cpiadrants 
were to be arranged in two circular arrays side by 
side on a spool with its axis of .symmetry lying in the 
horizontal plane. BDI indications in the plane de¬ 
fined by the instantaneous main axis of the scanning 
beam and the axis of symmetry of the spool were to 
be given by comparing the signals from the left and 
right circular arrays. The design called for a beam 
width in the BDI plane of 20 degrees at — G db. 

The “junction-box” rack was planned to contain 
the mica tuning condensers for the individual trans- 


CXJNFIDENTIAL 























































41^6 


CONSTRUCTION AND TESTING OF SCANNING TRANSDUCERS 


ducer elements, a “sum” scanning CR rotor, a “sum” 
listening CR rotor, a“ difference” scanning CR rotor 
to give the signal for BDI between the left and right 
banks of transducer elements, and arrangements for 
lifting the grounding bus bars of the condenser banks 
and the transformer banks during the pinging in¬ 
terval. 



Figure 33. Spool of the IIP-3DS transducer. 

The steel supporting spool is shown in Figure 33. 
The outside diameter of the flange rings is 23^ in. 
and the distance between the inside faces of these 
flanges is 9 in. The special “gooseneck” support was 
welded to a curved boiler plate which bolted on to 
the spool flanges over the upper back quadrant and 
matched a standard QC flange at the top. The mount¬ 
ing flange was designed to hold the spool in the po¬ 
sition in which the extended axis of the training 
shaft would pass through the axis of the spool. The 
mounting slots for the elements are shown on the in¬ 
side surfaces of the spool flanges. 

Figure 34A shows the spool with the transducer 
elements in place. The lead wires from the left bank 
of transducer stacks and the terminal board to which 
they are to be attached are shown, as are the 48 ele¬ 
ments that extend over 270 degrees of the circumfer¬ 
ence of the spool. The transducer cable was brought 


through a Rubber.seal watertight plug at the top of 
the gooseneck, through the gooseneck, into the center 
of the spool where the individual wires were splayed 
out, and soldered to the proper clips on the terminal 
board. Details of a single stack are shown in Fig¬ 
ure 35. 

The construction, testing, and assembly of the 
stacks to form the two stack elements were e.ssen- 
tially the .same as those described in the ca.se of the 
HP-3. 

Figures 34B and 34C show a later stage of con¬ 
struction and the transducer in its finished condition 
e.xcept for the side cover plate. The pair of large 
liands near each edge in Figure 34C were of stainless 
steel and were used to seal the edges of the rubber 
blanket to the flanges of the spool. The eight narrow 
bands in the center portion were of 0.010-in. haixl 
nickel. The.se bands were u.sed to hold the 3^-in. 
rubber blanket in firm acoustic contact with the 
active faces of the staves underneath. A film of castor 
oil was applied between the rubber faces of the ele¬ 
ments and the inner surface of the rubber blanket 
and another layer was applied between the nickel 
bands and the outer surface of the blanket to a.ssure 
acoustic contact. The nickel bands were drawn tight 
by the stainle.s.s-steel tiirnbuckles shown in the photo¬ 
graph. Tests made at Spy Pond showed this some¬ 
what complicated face a.s.sembly to be quite sati.s- 
factory. 

A full series of tests was carrietl out on the com¬ 
pleted transducer. The results of only a part of them 
need be presented here. In judging the patterns, it is 
well to note that the gooseneck causes considerable 
distortion of the sound field. 

The patterns recei^■ed through the sum listening 
rotor by rotating with the transducer at rest are 
shown in the .series of Figure 36 for transducer orien¬ 
tations, from the vertical, of 45, 90, 135, and 225 de¬ 
grees. The angular widths of these patterns are about 
as wide as would be expected from the angular 
span of each element. This resulted from the fact that 
the turntable of the pattern tracer was synchronized 
with the listening rotor in which the angular span 
of each condenser element was ;^3 times the angular 
span of each tran.sducer element. In fact, these pat¬ 
terns correspond exactly to the brightening presenta¬ 
tion on the plan position indicator [PPI] screen, with 
all the azimuthal angh* distortion resulting from the 
fact that the tran.sducer elements cover only of 
the circumference. 

The receiving pattern of all the elements in parallel 


CONFIDENTIAL 



SCANNING TRANSDUCERS BUILT AT HUSL 


447 



Figure 34. A. HP-3DS tran.?ducer with elements in place. B. End view showing element lead connections. C. Com¬ 
pleted transducer without end caps. 


CONFIDENTIAL 
























118 


CONSTKICTION AND TUSPINC; OF SCANNlNi; TKANSDUCKKS 



NODE 


ALUMINUM END CAP 


371/2-TURN, ^22 SCE WIRE 
WINDING, WOUND OVER 1/32" 
THICK BOOT OF AIR'CELL 
NEOPRENE WINDINGS EXTEND 
FROM NODE UP TO ABOUT 2/3 
OF THE LEG. 


+ LEAD WIRE 
POSITIONING BOSS 


I/I6"AIR-CELL NEOPRENE ISO¬ 
LATING PADS BETWEEN NICKEL 
CK AND ALUMINUM END 
CAPS. 


SLOT FOR PASSAGE 
OF WIRE DURING 
WINDING PROCESS 


3 3/^" 


ACTIVE FACE OF NICKEL STACK 
SINTERED OXIDE MAGNET- 


-LEAD 

WIRE 


P'lGURE 35. Detail of HP-3DS .stack. 


i.s .shown in Figure 37. The approximately .sinu.soidal 
fluctuations in the pattern should be noted. These 
have an amplitude of about ±2 db near the 0 and 
270 degree positions and about + 1 db in the center 
region (135 degrees). The average i.s very nearly uni¬ 
form over the 270 degrees of active surface. The 
period of the fluctuation i.s about 12 degrees of arc on 
the average. This corresponds clo.sely to the angle of 
11.3 degrees covered by two elements. The same 
period (i.e., the angular span of two elements) fluctu¬ 
ation of inten.sity with azimuth angle has been ob¬ 
served in the HP-1 and the HP-2 transducers. A 
theoretical study of the phenomenon was made in 
the case of the HP-2, from which it appeared that the 
fluctuations in the horizontal pattern could be ac¬ 
counted for by variation in impedance among the 
elements. Pha.se variation betw'een elements would 
tend to increase the intensity fluctuation. Although 
the elements in the HP-3DS transducer were rather 
carefully adjusted for impedance and were placetl 
around the spool in the order of their frequencies, 
the observed fluctuation of response or level with 
azimuth angle may be due to the variations in phase 
and impedance which remain. Calculations from the 
theory of the form of the jjatterns from a 270 degree 
sector for both pressure release and for stiff baffles 
show clo.se agreement between the calculated pat¬ 
terns and the ones observed. 


By using the method de.scribed for the HP-3 trans¬ 
ducer, the directivity index for a single HP-3DS 
element was found to be about 0.078. The measured 
recei^dng sensitivity was —95 db vs 1 volt per dyne 
per sq cm, and the i-esistive component of impedance 
was 19.5 ohms. The efficiency of a single stack com¬ 
puted from the.se data is about 0.30. 

With all 96 stacks connected in parallel with their 
condensers, as in transmitting, the directivity index 
was estimated to be 0.10, the resistive component of 
the impedance 0.27 ohm, and the receiving sen.sitivity 
was observed to be — 111 db vs 1 volt per dyne per 
sq cm. I'he.se values give a computed efficiency of 
0.42. During transmi.ssion with the same circuit con¬ 
nections, a voltage of 0.094 volt produced a fiekl of 
29 db vs 1 dyne per sq cm at 24 ft. If the imijedance 
is taken as 0.27 — jO.96 ohms and the directivity index 
as 0.10, the efficiency is 0.16. This latter value should 
not be considered as firm, however, because there was 
some question as to the exact value of the .sound field 
produced. 

The HP-3DS was built as an experimental unit in 
an integrated sonar system and installed as part of 
such a .system.'^ The design has, howevmr, certain in¬ 
herent defects. The goo.seneck connection with the 
training shaft is mechanically weak. The use of only 
three quadrants of the cylinder makes the problem 
of mounting and water-sealing the rubber blanket 


CONFIDENTIAL 




















SCANNIN(; TRANSDUCERS RUILT AT HUSL 


149 



Figure 36. Receiving patterns of IIP-SDS transducer for orientations of A, 45 degrees; B, 90 degrees; C, 135 degrees; 
D, 225 degrees, taken through sum listening rotor with transducer stationary. 


face unduly complicated. Howev'er, the tests showed 
that, in point of water tightness and acoustic trans¬ 
mission, the construction employed was .satisfactory. 
The measured phase difference between the gener¬ 
ated signal voltage in the various stacks and that in 
the stack on the acoustic axis was about 15 per cent 
greater than would be exjiected from simple wave 


theory, an effect that can probably be a.ssigned to 
acoustic baffling produced by the .size and .shape of 
the transducer itself. The receiving patterns through 
the lag line and C’R rotor were satisfactory, though 
not ideal. The side lobes were down by at least 12 db, 
and the back response was 25 db below that of the 
main lobe. The overall efficiency was about 0.30. 


CONFIDENTIAL 












































































CONSTRUCTION AND TESTING OK SCANNING TRANSDUCERS 


45(» 


The size of the HP-3DS was dictatofl by the pat¬ 
tern requirements for operation at the resonant fre- 
(}uency of 26 kc. Reduction in size is possible only by 
going to a higlier frequenc.y. Tliis was done ® in the 



Figure 37. Receiving pattern of HP-3DS traasducer, 
all elements in parallel. 


case of the HP-SId shown in Figures 11 and 35 of 
Chapter 13. In the HP-8D the resonant freciuency 
was 38 kc, and the diameter of the active face was 
15 in., as compared with the 173-'^ in. of the HP-3I)S. 
d'he lamination u.sed is .shown in Figure 46 of Chap¬ 
ter 13. Each stack in the two-stack element was 


3^2 j'l- long and the overall height of the elements 
was 7^16 in. Forty-eight elements were mounted in 
three (luadrants of the cylinder, the full surface of 
which was covered with a stretched rubber boot. In 
all respects, the design of the HP-8D is better than 
that of the HP-3DS. The construction and testing 
were e.s.sentially the same as those de.scribed in the 
case of the HP-3. Acoustic tests on the completed 
transducer showed an overall efficiency of approxi¬ 
mately 0.30. The vertical listening beam with the 
CR rotor and lag line was about 10 degrees wide, 
6 (lb down from the maximum, with the first minor 
lobes down 15 db and back radiation 22 db down 
from the major lobe maximum. 

14.7 SUMMARY 

During the later stages of the development of scan¬ 
ning .sonar transducers at HUSL, collaboration was 
maintained with the Sangamo Electric Company of 
Springfield, Illinois, in the building of three produc¬ 
tion models of the HP-5 transducer. This differed 
only in minor details from the HP-3. Sangamo’s ex¬ 
perience would .seem to bcai‘ out the statement that 
the various laboratory techniques described in the 
preceding section are applicable to ma.s.s production 
without demanding special skills on the part of man¬ 
ufacturing personnel. It is reasonably certain that 
with well-regulated and carefulh" .supervi.sed manu¬ 
facturing procedure, uniform products can be turned 
out without the multiplicity of detailed tests out¬ 
lined in the foregoing. In fact, it appears that the 
l)rea.ssembly testing might, under good manufactui- 
ing conditions, be waived entirely, since it is probable 
that changes taking place in the process of a.s.sembly 
are greater than the differences between well-built 
individual stacks before mounting. 


COXFIDENTIAL 




















GLOSSARY 


B 

B' 

B 

b 

C 


D 

I) 


(I 


E 

E 


E 


E' 


Eff 


F 

f 

fh h 

fr 

a 

G 


H 

i 

i 

i 

J 

K 

K 

k 


k 

L 

I 

M 


X 

P 

Pot eff 
P 


CHAPTERS 2 AND 3 


Radius. 

Magnetic induction {B, due to external field; 
Bo, polarizing). 

B-H (equation [4.2]). 

Electrical or mechanical susceptance (negative 
imaginary part of admittance, see Y). 

Radial thickness. 

Capacity. 

Speed of sound (usually c in water, Cm in mag- 
netostrictive core). 

Directivity ratio. 

Diameter of motional circle (subscripts A, air; 
ir, water; Z, impedance circle; admittance 
circle). 

Length characteristic of penetration of eddy 
currents. 

Potential, voltage. 

Young’s modulus {E', modulus with magneto- 
strictive coupling). 

Point of maximum efficiency in impedance or 
admittance diagram. 

Point of maximum conductance in admittance 
diagram. 

Efficiency of transducer in converting electrical 
to mechanical power. 

Voltage representing force in equivalent circuit. 

Force. 

Frequency (subscripts 0, center; 1, 2, “3 db”; 
E, maximum efficiency; R, resonance). 

Frequencies at which rod is 34, 34 "‘ave length. 

Characteristic frequency for eddy-current effects. 

Electromechanical mutual impedance for rod. 

Conductance, Gmax, Gm\,„ maximum and mini¬ 
mum conductances on admittance loop 
(see FI- 

Magnetic field, H,: field applied externally. 

Intensity of magnetization, (B — H)Air. 

Current. 

Current representing velocity in equivalent 
circuit. 

Reciprocity parameter (J,, at one meter). 

Stiffness, /voi stiffness without magnetostrictive 
colliding. 

Image impedance of constant-K filter at mid¬ 
band. 

Coefficient of electromechanical coupling; kou- 
effective coefficient of electromechanical 
coupling. 

Wave number = 27r'(wave length). 

Inductance, Lo'. inductance of core at low fre¬ 
quencies. 

Length. 

Mass, Mf., mass of plate per tube. Section 3.44; 
nio, ma.ss of tube Mtt of wave length, Sec¬ 
tion 3.44. 

Number of turns around core. 

Longitudinal stress. 

Potential efficiency. 

Pre.ssure. 


P 

Q 


R 

R 


(f/fo -/o//)/2. 

Electrical or mechanical sharpness of resonance 
(subscripts A, air, IF, water; Z, impedance 
data; F, admittance data; c, core; e, blocked 
electrical, etc.). 

Pllectrical or mechanical resistance; Rmax, Rmin, 
maximum and minimum resistances on im- 
Iiedance loop (see Z). 

Resonance. 

Distance between transducer and point of ob¬ 
servation or distance between two transducers. 


s 

t 

t 

Tv 

V 

IF 

X 

X 

1 


Sv, Si Open-circuit voltage and short-circuit current 
sensitivities. 

Longitudinal strain. 

Thickness of lamina. 

Time. 

Tj Voltage and current transmitting responses. 
V'elocity of radiating surface of transducer. 
Potential energy per unit volume. 

Electrical or mechanical reactance. 

Distance. 

= G — jB Electrical or mechanical admittance; F, = \'Z„ 
blocked electrical admittance; F, = l/Zi, 
loaded electrical admittance; Fmot = F, — Fo, 
motional admittance; Fc = 1 Zc, core ad¬ 
mittance. 

Z = R +jX Electrical or mechanical impedance; Z„ blocked 
electrical impedance; Z,-, loaded electric im¬ 
pedance; Zmot = Zi — Ze, motional imped¬ 
ance; Zm = ZL + Zm, open-cu'cuit mechanical 
impedance; Zm, mechanical impedance with¬ 
out magnetostrictive coupling; Zm, additional 
mechanical impedance produced by coupling; 
Zl, mechanical load impedance, radiation 
impedance; Zc, core impedance; Z;, leakage 
impedance. 

e Magnetostrictive coefficient, equation (3) ff. 

Negative phase of eddy-current factor (see x). 
Phase angles related to Z„ Z^m, [see equation 
(59)]. 

Pha.se lag due to hysteresis. 

(dB'/dp) at constant H. 

Wave length in water, equation (88)ff.; mag¬ 
netostrictive constant, equation (lO)ff. 
Permeability (clamped core). 

Permeability at constant stress. 

Displacement. 

Density (usually p for water, pm for magneto¬ 
strictive core). 

Specific acoustic resistance. 

Pllectric resistivity. 

.4rea (usually <r for radiating face, am for core 
section). 

Effective area, equation (92). 

Magnetic flux. 

Turns ratio of ideal transformer. 

= A’r — fl = A'oC'j' Eddy-current factors. Section 3.1. 

= 2ir/ Angular frequency. 


f 

■n 

A 

X 

M 

X 

p 

pc 

pc 


<!> 

A' 


CONFIDENTIAL 


4 . 11 


452 


GLOSSARY 


GENERAL 


Acoustic Axis. Reference line adopted in transducer calibra¬ 
tion, usually the direction of maximum response. 

B.^ffle. a shield used to modify an acoustic path. 

B. \ffle, Rei.e.\se. baffle satisfying the boundary condition 

of zero v'ariational pressure. 

Baffle, Stiff. .\n ideally rigid baffle. 

BDI. Bearing deviation indicator. 

Bearing Devi.ation I.nuicator. .\ system which utilizes the 
outputs of the halves of a split transducer to provide ac¬ 
curate bearing indication. 

BTL. Bell Telephone Laboratories. 

C. AViT.ATioN. The formation of vapor or gas cavities in water, 
caused by sharp reductions in local pressure. 

CR System. Commutated-rotation scanning sonar. 

Crystal Transducer. .\ transducer which utilizes piezo¬ 
electric crystals, usually Rochelle Salt, .\DP, quartz, or 
tourmaline. 

Curie Point. The temperature above which a ferromatic 
substance becomes paramagnetic. The Curie point for iron 
is 769 C, for nickel 356 C. 

Cyclicly' Magnetized. magnetic material is in a cyclicly 
magnetized condition when it has been under the influence 
of a magnetizing force varying between two specific limits 
until, for each increasing or decreasing value of the mag¬ 
netizing force, the magnetic induction has the same value 
in successive cycles. 

DCDI. Depth charge direction indicator. 

Directivity Index. .\ measure of the directional properties 
of a transducer. It is the ratio in decibels of the average 
intensity or response over the whole sphere surrounding the 
projector or hydrojihone to the intensity or response on the 
acoustic ivxis. 

Directivity R.atio. A measure of the directional properties 
of a transducer. It is the numerical ratio of the intensity or 
response on the acoustic axis to the average intensity or 
response over the whole sphere surrounding the jirojector 
or hydrophone. 

Dome. A transducer enclosure, usually streamlined, used with 
echo-ranging or listening devices to minimize turbulence and 
cavitation noises arising from the transducer’s passage 
through the water. 

DRSB. Directional radio sono buoy. 

Echo Repeater, .\rtificial target, used in sonar calibration 
and training, which returns a synthetic echo by receiving, 
amplifying, and retransmitting an incident ping. 

ERSB. Ex|)endable radio sono buoy. 

HP-Ty'pe Tr.xnsducer. Hebb phone, a longitudinally vi¬ 
brating laminiited stack transducer of tyiic used in final 
QH design. 

H-RLP. Harvard ring ladder|)hone. 

IIUSL. Harvard Underwater Sound Laboratory. 

Hydrophone. Underwater microphone. 

JP. A submarine listening system employing magnetostriction 
line hydrophone. 

Magnetocaloric Effect. Changes in magnetism with tem- 
jierature changes. 

M.agnetomotive Force. Magnetic analogue of electromotive 
force. 


M.xg.netostriction Effect. Phenomenon exhibited by cer¬ 
tain metals, particularly nickel and its alloys, which change 
in length when magnetized, or, (Villari Effect) when mag¬ 
netized and then mechanically distorted, and undergo a 
corresponding change in magnetization. 

Neoprene. Generic name for synthetic rubber made by 
polymerization of 2-chloro-l, 3-butadiene. Vulc:inizates are 
markedly resistant to oils, greases, chemicals, sunlight, 
ozone, and heat. 

0.\X Monitor. portable sound gear monitoi', with range 
from 15 kc to 2() kc. 

OC'P Monitor. portable sound gear monitor, with range 
from 10 kc to 70 kc. 

Permendur. Alloy of iron, cobalt, and not more than 2% 
vanadium which maintains uniformly high permeability to 
alternating flux in the presence of a superposed polarizing 
flux. 

Piezoelectric Effect. Phenomenon exhibited by certain 
crystals in which mechanical compression produces a 
potential difference between opposite crystal faces or an 
aiiplied electric field jiroduces corresponding changes in di¬ 
mensions. 

Pi.NG. .Vcoustic pulse signal jirojected from echo-ranging 
transducer. 

PPCR. Portable iiolar chart recorder. 

PPL Plan position indicator. 

Pre.sscre Release. Material, such as air-cell rubber, in¬ 
capable of supporting variational acoustic pre.ssure. 

Projector. .\n underwater acoustic transmitter. 

QH. Navy designation for scanning sonar of CR type using 
magnetostriction transducer. 

pc Rubber. rubber compound with the same pc (density 
X velocity of .sound) product as water. 

Ring Stack. A magnetostrictive transducer composed of ring 
laminations which vibrate radially. 

Sc.ANNi.NG SoN.AR. Echo-rangiiig system in which the ping is 
transmitted simultaneously throughout the entire angle to 
be searched and a rapidly-rotating narrow beam scans for 
the returning echoes. 

Searchlight-Type Son.ar. Echo-ranging system in which the 
same narrow beam pattern is used for transmission and 
reception. 

SGM. Sound gear monitor. 

SoN.YR. Generic term ap()lied to methods or apparatus that 
use SOund for N.\vigation and Ranging. 

Sonic Freguencies. Range of audible frequencies, .sometimes 
taken as from .02 kc to 15 kc. 

Sono Buoy. A buoy listening device that contains a hydro¬ 
phone for receiving target signals and a radit) transmitter for 
relaying the signals to patrolling air or surface craft. 

SPEP OR SP-Type Tran.sducer. .\ small longitudinally- 
vibrating laminated stack transducer element, having 
permanent magnet iiolarization. 

SSL Sector scan indicator. 

St.acks, L.ymin.ated. Pile of consolidated laminations. 

Stave. Individual longitudinal transducer element, a number 
of which make up a sonar transducer. 


CONFIDENTIAL 



GLOSSARY 


453 


Supersonic Frequencies. Range of frequencies higher than 
sonic. Sometimes referred to as ultrasonic to avoid con¬ 
fusion with growing use of the term supersonic in connec¬ 
tion with higher-than-sound velocities. 

Transducer. Any device for converting energy from one 
form to another (electrical, mechanical, or acoustical). In 
sonar, it usually combines the functions of a hydrophone 
and a projector. 

Tube-and-Cone. a transducer element using a magneto¬ 
striction tube to drive a radiating cone. 

Tube-.and-Plate. a transducer using one or more magncto- 


strictive tubes to drive a flat diaphragm, as in the QC 
transducer. 

Tubular-Type Transducer. Thin-walled magnetostrictive 
tube which vibrates radially. 

“Turk’s Head.” A stainless-steel woven wire covering used 
to hold the protective rubber boot in place over the trans¬ 
ducer. 

V.\LP. V'ector admittance locus plotter. 

ViLL.ARi Effect. The inverse magnetostriction effect. 

VILP. Vector impedance locus plotter. 

VTVM. Vacuum tube voltmeter. 


CONFIDENTIAL 



t 



Tifmt 


_Fill 




ja 




'!• f' 

V 


» <1 



/• 


F 



-•F 







t 


» 



tu 




14 


■ i 



BIBLIOGRAPHY 


Numbers such as Div. 6-551-M3 indicate that tiie document listed has been microfilmed and that its title appears in 
the microfilm index printed in a separate volume. For access to the index volume and to the microfilm, consult the 
Army or Navy agency listed on the reverse of the half-title page. 


Chapter 1 

1. Absolute Efficiency of Projectors and Hydrophones, Figin- 15. 
hard Dietze, NDRC C4-sr20-150, USRL, Aug. 3, 1942. 

Div. 6-551-M3 

2. The Absolute Efficiency of a Device Used as a Projector and 
as a Hydrophone, Eginhard Dietze, NDRC C4-.sr20-197, 

USRL, Aug. 18, 1942. Div. 6-551-M4 10. 

3. The Relation between the Absolute Efficiency of a Hydro¬ 


phone and Its Thermal Noise Level, Eginhard Dietze, 

OSRD 1086, NDRC C4-sr20-593, USRL, Dec. 11, 1942. 17. 

Div. 6-552-M5 18. 

4. Magnctostrictive Transducers, Malcolm H. Hebb, Harvey 

A. Brooks, NDRC 6.1-sr287-898, HITSL, June 22, 1943. 19. 

Div. 6-612.1-M2 

5. Open-Circuit Frequency Response of Parallel Tuned 

Transducer (Memorandum), Malcolm H. Hebb, HUSI^, 20. 

Nov. 16, 1943. Div. 6-612.23-M2 

6. Measurement of Projector and Hydrophone Performance, 

Definition and Terms, Eginhard Dietze, NDRC 6.1- 21. 

srll30-[1833], NS-182, USRL, Sept. 19, 1944. 22. 

Div. 6-551-Ml2 

7. Q and the BTL, Malcolm FI. Hebb, M 01.10-172, HFhSL, 

Mar. 12, 1945. Div. 6-612.34-M7 23. 

8. Scanning Sonar, Summary Technical Report, NDRC 

Division 6, Vol. 16, Chap. 5. 24. 

9. Computation of Absolute Efficiency of a Hydrophone from 
Its Sensitivity, Flginhard Dietze, Report 2420-F:D-F, 

BTL, Aug. 29, 1941. Div. 6-612.22-M2 25. 


10. Relation between Power Delivered by a Hydrophone and 

Its Absolute Efficiency, Flginhard Dietze, Report 2420- 26. 

ED-LA, BTL, Aug. 29, 1941. Div. 6-612.22-Ml 

11. Absolute Efficiency of Hydrophones, Flginhard Dietze, 

Report 2420-ED-EN, BTL, Oct. 18, 1941. 

Div. 6-612.22-M3 27. 

12. Hydrodynamic Listening Devices, Eginhard Dietze, 


Walter D. Goodale, Jr., Report 2420-ED-WDG-KM, 28. 

BTL, Dec. 3, 1941. Div. 6-612.1-Ml 

13. Hydrodynamic Instruments, A. H. Inglis, Report 2240- 29. 

AHI-VD, BTL, Dec. 13, 1941. Div. 6-612..54-M1 30. 

14. “On the Effects of Magnetism upon the Dimensions of 31. 
Iron and Steel Bars,” J. P. Joule, Flsq., The London, 
Edinburgh and Dublin Philosophical Magazine and 32. 
Journal of Science, Ser. 3, Vol. 30, January to June 1847, 

pp. 225-241. 


(-hapter 2 

1. Equivalent Circuits for Electromechanical Transducers, 3. 
Edwin M. McMillan, HUSL File SD 29, UCDWR, 

Jan. 10, 1942. Div. 6-612.31-Ml 

2. Optimum Coupling between Microphones and Amplifiers, 4. 
William B. Snow, Report G12/2805, CUDWR-NLL, 

May 15, 1942. Div. 6-612.33-Ml 


“Ueber die Aenderungen des Magnetischen Moments, 
Welche der Zug und das Hindurchleiten Flines Gal- 
vanischer Stroms in Fhnem Stabe von Stahl oder Eisen 
Hervorbringen,” E. Villari, Annalen der Physik und 
Chemie, J. G. Poggendorff, Vol. 126, 1865, pp. 87-142. 
Magnetic Induction in Iron and Other Metals, Sir James 
Alfred Flwing, D. Van Nostrand Co., Inc., New V'ork, 
N. Y., 1891. 

British Patent 145,691, P. Langevin, 1920. 

Unterwasser Schalltechnik, FTanz Aigner, M. Krayn, 
Berlin, Germany, 1922. 

Transmission Circuits for Telephone Communications, 
K. S. Johnson, D. Vhan Nostrand Co., Inc., New V'ork, 
N. Y., 1925, pp. 32, 33. 

Theory of Vibrating Systems and Sound, 1. B. Crandall, 
D. Van Nostrand Co., Inc., New York, N. Y., 1927, 

p. 118. 

U. S. Patent 1,750,124, G. W. Pierce, 1927. 

“A Dynamic Study of Magnetostriction,” K. C. Black, 
Proceedings of the American Academy of Arts and 
Sciences, Ser. 2, Vol. 53, 1928. 

“Magnetostriction,” A. Schulze, Zeitschrift fur Physik, 
Vol. 50, 1928, pp. 448-505. 

“Magnetostriction Oscillator,” G. W. Pierce, Proceedings 
of the American Academy of Arts and Sciences, Vol. 63, 
1928, p. 1. 

Magnetic Properties of Matter, Kotaro Honda, Syokwabo 
and Co., Tokyo, Japan, 1928. 

“Reciprocity in Electromagnetic, Mechanical, Acoustical 
and Interconnected Systems,” Stuart Ballantine, Pro¬ 
ceedings of the Institute of Radio Engineers, Vol. 17, 
June 1929, pp. 929-951. 

Magnetic Phenomena, Samuel R. Williams, McGraw- 
Flill Book Co., Inc., New York, N. Y., 1930. 

Fairlie Magnetostriction Reports, F. D. Smith, HL^SL 
File B[ritish 10], 1931. 

LL S. Patent 2,005,741, H. C. Hayes, June 25, 1935. 

FT. S. Patent 2,063,951, R. L. Steinberger, Dec. 15, 1936. 
Alloys of Iron and Nickel {Monograph Series), J.S. March, 
McGraw-Hill Book Co., Inc., New York, N. Y., 1938. 
“Impedance of Telephone Receivers as Affected by the 
Motion of Their Diaphragms,” A. E. Kennedy, G. W. 
Pierce, Electrical World, Sept. 14, 1942. 


Relation between Sensitivity and Efficiency of a Hydro¬ 
phone, Harvey Brooks, M 01.213-10, HUSL, Dec. 4, 
1942. Div. 6-612.22-M6 

Motional Impedance Analysis of Underwater Sound De¬ 
vices, F'rank H. Graham, Eginhard Dietze, NDRC 
C4-sr20-591, USRL, Dec. 5, 1942. Div. 6-551-M7 


CONFIDENTIAL 


45.5 


456 


kibli(k;k\phv 


5. Shock Excitation of Resonant Transducers, Harvey A. 
Brooks, M 01.213-12, HUSL, Dec. 17, 1942. 

Div. 6-6r2.22-M7 

6. Efficiency of Maynetostrictive Transducers, Harvey A. 
Brooks, M 01.213-25, HUSL, Jan. 19, 1943. 

Div. ()-612.22-M9 

7. Theory of Passive Linear Electromechanical Transducers, 

Leslie L. Foldy, NDRC 6.1-sr20-878, Xavy Project NS- 
139, USRL, June 9, 1943. Div. 6-551-MlO 

8. Magnetostrictive Transducers, Malcolm H. Hehh, Harvey 
A. Brooks, XDRC 6.1-sr287-898, HUSL, June 22, 1943. 

Div. 6-612.1-M2 

9. Figure of Merit for Magnetostrictive Transducers, Harvey 

A. Brooks, Malcolm H. Hebb, M 01.213-50, HUSL, 
June 29, 1943. Div. 6 612.22-MlO 

10. .4 Simplified Method of Computing Potential Efficiencies 
(Memorandum), Harvey A. Brooks, IH'SI,, Sept. 30, 
1943. Div. 6-612.22 Mil 


11. Further Generalization of the Concept of Potential Effi¬ 
ciency Applicable to Any Resonant Transducer (Memo¬ 
randum), Harvey .\. Brooks, lirSI,, Oct. 1, 1943. 

Div. 6-612.22-M12 

12. Motional Admittance (Memorandum), Malcolm H. 

Hebb, HUSL, Xov. 20, 1943. Div. 6-612.3-M2 

13. Reciprocity of Linear Electromechanical Systems (Memo¬ 
randum), Malcolm H. Hebb, HUSL, Dec. 8, 1943. 

Div. 6-612.512-M5 

14. The Geometrical Inversion Transformation and Its Ap¬ 

plication in the Admittance-Impedance Relations, Analyti¬ 
cal Admittance-Impedance Relations (Memorandum), 
Robert Pi. Payne, Malcolm H. Hebb, HUSL, Jan. 26, 
1944. Div. 6-612.32-Ml 

15. Electrodynamic Transducers for Supersonic Underwater 

Sound, Malcolm H. Hebb, M 01.214-10, HUSL, Sept. 
13,1944. Div. 6-612.1-M7 


Chapter 3 


1. Equivalent Circuits for Electromechanical Transducers 

(Preliminary Draft), Pidwin M. McMillan, UCDWR, 
Jan. 10, 1942. Div. 6-612.31-Ml 

2. Equivalent Circuit of Magnetostriction Oscillators, Harvey 

Brooks, M 01.10-12, HUSL, June 5, 1942. 

Div. 6-612.31-M2 

3. Efficiency of Magnetostriction Transducers, Malcolm H. 
Hebb, M 01.213-3, HUSL, Aug. 14, 1942. 

Div. 6-612.22-M5 

4. Series and Parallel Tuning of Transducers, Malcolm H. 
Hebb, M 01.213-7, PIUSL, Oct. 13, 1942. 

Div. 6-612.31-M3 

5. Laminated Magnetostriction Tubes, Malcolm H. Hebb, 
M 01.213-7.1, ilUSL, Xov. 7, 1942. Div. 6-612.63-Ml 

6. The Alleged Failure of Reciprocity in Electroacoustical 

Systems, P'rederick V. Hunt, M 01.213-8, IH'SL, Xov. 
30,1942. Div. 6-612.512-Ml 

7. Elementary Results Regarding Tuning of Magnetostriction 

Microphones, Haivey .V. Brooks, M 01.213-9, HUSL, 
Dec. 1, 1942. Div. 6-612.31-M4 

8. Relation between Sensitivity and Efficiency of a Hydro¬ 

phone, Harvey .4. Brooks, M 01.213-10, HUSL, Dec. 4, 
1942. Div. 6-612.22-M6 

9. Motional Impedance Analysis of Underwater Sound De¬ 
vices, Frank H. Graham, Pi^iidiard Dietze, XDRC, 
C4-sr20-.591, USRL, Dec. 5, 1942. Div. 6-551-M7 

10. Shock Excitation of Resonant Transducers, Harvey .\. 
Brooks, M 01.213-12, HUSL, Dec. 17, 1942. 

Div. 6-612.22-M7 

11. Efficiency and Sensitivity of Cone-Type Magnetostriction 

Transducers, Harvey .\. Brooks, M 01.213-18, HUSL, 
Jan. 4, 1943. Div. 6-612.22-MS 

12. Frequency Response Curves, Malcolm H. Hel)b, M 01.- 

213-20, HUSL, Jan. 7, 1943. Div. 6-612.51 -M 1 

13. Efficiency of Magnetostrictive Transducers, Harvey 
Brooks, M 01.213-25, HUSL, .Jan. 19, 1943. 

Div. 6-612.22-M9 


14. Capacity of Ground in Calibration of Transducers, Harvey 

A. Brooks, Malcolm H. Hebb, M 01.10-27, HUSL, Feb. 
1, 1943. Div. 6-612.51-M2 

15. Theory of Passive Linear Electromechanical Transducers, 

Leslie I.. P'oldy, XDRC, 6.1-sr20-878, Xavy Project 
XS-139, USRL, June 9, 1943. Div. 6-551-MlO 

16. Magnetostrictive Transducers, Malcolm H. Hebb, Harvey 
A. ikooks, XDRC, 6.1-sr287-898, HUSI., June 22, 194^ 

Div. 6-612.1-M2 

17. Figure of Merit for Magnetostrictive Transducers, Harvey 
» A. Brooks, Malcolm H. Hebb, M 01.213-.50, HUSL, 

June 29, 1943. Div. 6-612.22-MlO 

18. Equivalent Circuit for Magnetostrictive Transducers 

(Memorandum), Malcolm H. Hebb, HUSI^, July 12, 
1943. Div. 6-612.31-M5 

19. Reduction of Eddy Currents in Magnetostrictive Tubes, 
Malcolm H. Hebb, M 01.213-62, HUSL, July 24, 1943. 

Div. 6-612.8-M4 

20. .4 Simplified Method of Computing Potential Efficiencies, 
Harvey A. Brooks, M 01.213-86, HUSI., Sept. 30, 1943. 

Div. 6-612.22-Mll 

21. Further Generalization of the Concept of Potential Efficiency 
Applicable to Any Resonant Transducer, Harvey A. 
Brooks, M 01.213-88, HUSL, Oct. 1, 1943. 

Div. 6-612.22-M12 

22. Some Geometrical Relalions in the Impedance Diagram, 
James W. Follin, Jr., M 01.213-92, HUSL, Oct. 11, 1943. 

Div. 6-612.511-M6 

23. Magnetostrictive Transducers, Representation of Solid 
Horn by Four-Terminal Network, Malcolm H. Hebb, 
M 01.213-107, HUSl., Xov. 3, 1943. Div. 6-612.3-Ml 

24. Motional Admittance, Malcolm H. Hel)b, M 01.213-113, 

HUSL, Xov. 20, 1943. Div. 6-612.3-M2 

25. Measurements on }i-in. 20-kc Ring Stack, James W. 
Follin, Jr., M 01.213-115, HUSL, Xov. 20, 1943. 

Div. 6-612.61-M4 


CXJXFIDEXTIAL 



BIBLIOGRAPHY 


■to? 


20. Reciprocity of Linear Electromechanical Systems, Malcolm 

H. Hehb, M 01.213-125, HUSL, Dec. 8, 1943. 

Div. 6-612.512-M5 

27. Determination of E, X, and Electromechanical Coupliny 

Coefficient from Impedance Data, S. T. Pan, M 01.213-130, 
HUSL, Dec. 22, 1943. Div. 6-612.51-M5 

28. The Geometrical Inversion Transformation and Its Ap¬ 
plication in the Admittance-Impedance Relations, Analyti¬ 
cal Admittance-Impedance Relations, Robert E. Payne, 
Malcolm H. Hebb, M 01.213-141, HUSL, .Ian. 20, 1944. 

Div. e-012.32-Ml 

29. Band-Pass Characteristics of Maynetostrictive Transducers, 

Malcolm H. Hebb, Nelson M. Blachman, M 01.213-142, 
HCSL, .Jan. 28, 1944. Div. e-012.34-Ml 

30. Relation between Electromechanical Coupliny and DQ '\7jc\, 
Malcolm H. Hebb, M 01.213-153, HUSL, Feb. 10, 1944. 

Div. 0-012.31-M0 

31. Methods of Obtaininy Band-Pass Characteristics with 
Maynetostriction Transducers, .James W. Follin, .Jr., 
M 01.21.3-1.55, HUSL, Feb. 17, 1944. Div. 0-G12.34-M2 

32. Band-Pass Transducers, Frederick V. Hunt, M 01.213- 

I. 58, lirSI., I'eb. 19, 1944. Div. 6-ei2.34-M3 

33. Elimination of Eddy Currents in Maynetostriction Hydro¬ 

phones, .James W. Follin, .Jr., Iteport G12/742, NS-139, 
Cri4\VR-NI.L, Feb. 24, 1944. I4iv. e-ei2.31-M7 

34. Some Qualitative Notes on Band-Pass Transducers, Ben¬ 
jamin 13. Drisko, M 01.213-109, HUSI., Mar. 8, 1944. 

Div. e-012.34-M4 

35. Coupliny Tests on Seymented and Vnseymented Ladder- 

phone Stacks, LDPI No. 1 and No. 2, William T. 
Bartholomew, Francis P. Bundy, M 01.213-173, Hl'SJ., 
Mar. 10, 1944. Div. 6-612.31-M8 


30. Band-Pass Transducers, Malcolm H. Hebb, Nelson M. 
Blachman, M 01.213-170, HUSL, Mar. 23, 1944. 

Div. e-012.34-M.5 

37. Transducers Separated from the Water by Rubber or Oil, 
Nelson M. Blachman, M 01.21-72, HUSL, May 12, 1944. 

Div. e-ei2.43-M0 

38. Lamination Desiyn to Minimize the Q, Nelson M. I31ach- 
man, M 01.213-200, HUSL, .June 17, 1944. 

Div. 0-012.34-M6 

39. Impedance Diayram for Parallel Tuned MS Transducer, 
Malcolm H. Hebb, M 01.213-205, HUSI>, .June 28, 1944. 

I3iv. e-ei2.32-M3 

40. Compressed Metallic Dust as a Maynetostrictive Material, 

William T. Bartholomew, Francis P. I3undy, M 113.5- 
147, HUSL, .July 7, 1944. I4iv. 6-612.42-M8 

41. Equivalent Circuit for Maynetostrictive Transducers, 
Robert E. Payne, M 01.213-213, Hl'SL, Aug. 3, 1944. 

Div. 0-012.31-M9 

42. Tests and Analysis of British Scanning Sonar Transducer 

Element, Francis P. Bundy, M 02.45.7-120, HUSL, 
Oct. 25, 1944. Div. e-612.55-MlG 

43. Equalization of Hydrophones, Nelson M. Blachman, 
M 01.21-101, HUSL, Oct. 31, 1944. Div. e-ei2.31-M10 

44. Q and the BTL, Malcolm H. Hebb, M 01.10-172, HUSL, 

Mar. 12, 1945. Div. e-G12.34-M7 

45. Transducer Research and Production at the New London 
Laboratory, William B. Snow, .James W. Follin, .Jr., 
Wilbur T. Harris, NDRC G.l-srl 128-2212, Report 
012 1418, NS-113, CUDWR-NLL, May 25, 1945. 

Div. e-612.1-M8 

40. Electromechanical Transducers and Wave Filters, W. P. 
Mason, D. Van Nostrand Co., Inc., New York, N. Y., 
1942, Section 0.5. 


(Chapter 4 


1. Measurements of the Permeability of Maynetostrictive 

Materials, Howard C. Hardy, M 01.213-23, HUSL, 
.Jan. 14, 1943. I3iv. G-ei2.4-M2 

2. Properties and Uses of Alnico Magnets, Kenneth N. 

Fromm, J’rancis P. I3undj', M 01.213-35, HUSL, Apr. 
23, 1943. Div. 0-ei2.42-Ml 

3. Magnetostrictive Transducers, Malcolm H. Hebb, Harvey 
A. Brooks, NDRC e.l-sr287-898, HUSL, .June 22, 1943. 

Div. e-ei2.1-M2 

4. Acoustic Properties of Hydrogen Annealed Nickel, Nelson 

K. Moody, .Jr., Harvey A. Brooks, M 113.5-28, HUSIj, 
.July 5, 1943. Div. e-012.41-M2 

5. Visit to Laboratory of E. M. JUise of the International 

Nickel Company, Inc., on July 13, 19.^3, Malcolm H. 
Hebb, Francis P. Bundy, M 113..50-37, HUSL, .July 27, 
1943. Div. 0-012.41-M3 

0. Nickel Alloys for Transducers, Frederick V. Hunt, 
M 113..50-39, HUSL, .July 30, 1943. Div. 0-012.41-M4 

7. Tests on Hydrophones with Shells Specially Heat Treated 
by C. G. Conn, Ltd., Robert R. Macl.aughlin, Report 
DlO/473, NS-102, CUDWR-NLL, Aug. 11, 1943. 

Div. 0-012.41-M5 

8. Nickel Strip Material, .Alan 11. Selker, M 113.50-10, 

HUSL, Aug. 24, 1943. Div. G-ei2.41-M0 


9. Heal Treatment of Nickel, Robert R. MacJjaughlin, Re¬ 
port 012/5.30, CUDWR-NLL, Sept. 14, 1943. 

Div. e-ei2.41-M7 

10. Visit to JJ'esJ Lynn Laboratory of General Electric regard¬ 
ing Materials for Permanent Magnets, F'rancis P. Bundy, 
M 113.50-.59, Hl^SL, Sept. 2.5, 1943. Div. e-ei2.42-M2 

11. Measurements of 5-in. Toroidally Wound Magnetostriction 

Hydrophones, Evaluation of Annealing of Nickel, Edward 
Gerjuoy, Wilbur T. Harris, Report DlG/555, CUDWR- 
NLL, Oct. 19, 1943. Div. G-ei2.41-M8 

12. Magnetic Properties and Electrical Resistivities of Oxide 
Annealed and Cold-Worked Nickel [Grade] A, S. T. 
Pan, M 113..50-73, HUSL, Nov. 8, 1943. 

Div. e-G12.41-M9 

13. Visit to Bell Telephone Laboratories, November 18 and 19 

[L9.^S], Francis P. Bundy, M 113..50-79, HUSL, Nov. 
27, 1943. Div. e-G12.4-M3 

14. Visit to Bell Telephone Laboratories, November 18 and 19 

.James W. lM)llin, ,Jr., M 113..50-S2, HUSL, Dec. 3, 
1943. Div. 0-012.4-M4 

15. Determination of E, X, and Electromechanical Coupling 

Coefficient from Impedance Data, S. T. Pan, M 01.213- 
130, HUSI., Dec. 22, 1943. Div. G-G12.51-M5 


(CONFIDENTIAL 




458 


HIBLIOGRAPHV 


16. General Magneiic Properties and Magnetostrictive Proper¬ 
ties of Hydrogen-Annealed 0.005" Jt5-Permalloy Sheets, 
S. T. Pan, M 113.50-93, HUSL, Jan. 15, 1944. 

Div. 6-612.42-M3 

17. Magnetic Properties of [Grade] A Nickel for Use in 

Laminated Stack Transducers, James W. Follin, Jr., S. T. 
Pan, NDRC, 6.1-sr287-1352, H-234, HUSL, Jan. 25, 
1944. Div. 6-612.41-M13 

18. The 8 Va Vicalloy, S. T. Pan, M 113.50-98, HUSL, 

Feb. 15, 1944. Div. 6-612.42-M4 

19. Annealing of JP-1 Straight Wood Core Hydrophone, 
Hector F. Bernier, Report G12/753, XS-139 and NS-113, 
CUDWR-NLL, Feb. 26, 1944. Div. 6-612.41-M16 

20. The 2 V Permendur, S. T. Pan, M 113.50-104, HUSL, 

Mar. 14, 1944. Div. 6-612.42-M5 

21. Grade A Nickel Annealed in Hydrogen, S. T. Pan, 
M 113.50-112, HUSL, Apr. 13, 1944. 

Div. 6-612.41-M17 

22. Bieber’s Alloy, S. T. Pan, M 113.50-119, HUSL, A])r. 26, 

1944. Div. 6-612.42-M6 

23. Magnetic Properties of 45 Permalloy, S. T. Pan, B. A. 

Wooten, NDRC 6.1-sr287-1542, H-264, HUSL, Apr. 30, 
1944. Div. 6-612.42-M7 

24. Self-Polarized Ring Stacks, Francis P. Bundy, G. W. 
Renner, M 01.213-194, HUSL, May 9, 1944. 

Div. 6-612.61-M9 

25. Effect of Annealing on the Magnetic Properties of Nickel 

Tubing (Memorandum for bdle), Arthur !>. Thuras, 
James W. Follin, Jr., Report G12/928, Cl"DWR-\LL, 
May 16, 1944. Div. 6-612.41-M19 

26. Half-Hard Grade A Nickel, S. T. Pan, M 113.5-145, 

HUSL, .July 6, 1944. Div. 6-612.41-M20 

27. The 6.5 V Vicalloy, S. T. Pan, M 113.5-1.50, HUSL, 

July 12, 1944. Div. 6-612.42-M9 

28. TFeston Permalloy Powder Cores, S. T. Pan, M 110.5-102, 

HUSL, July 19, 1944. Div. 6-612.42-MlO 

29. The 2-V Permendur Hydrophones, Wilbur T. Harris, 
David W. Van Lennei), Phillip B. Edwards, Report 
G12/n68, NS-102, CUDWR-NLL, Oct. 6, 1944. 

Div. 6-612.8-M16 

30. Test Equipment and Methods for Relative Permeability 
Measurements on Nickel Tubing (Memorandum for File), 
Robert R. Macljaughlin, Report G12 1230, NS-102, 
CUDWR-NLL, Nov. 10, 1944. Div. 6-612.8-M18 

31. Variation of Magnetization in Legs of PM Polarized 

SPEP Element ivith Driving Field, S. T. Pan, M 01.213- 
291, HUSL, Dec. 6, 1944. Div. 6-612.41-M21 

32. Reversible Permeability and Hysteresis Loss in Oxide- 
Annealed [Grade] A Nickel Polarized at Bo = JJOO, 
S. T. Pan, M 113.5-180, HUSL, Dec. 12, 1944. 

Div. 6-612.41-M22 

,33. .4 Detailed Study of Sintered-Oxide Magnets in HP-3 


Stacks, S. T. Pan, Milton R. Carlson, Francis P. Bundy, 
M 01.213-28.5, HUSL, Dec. 1.5, 1944. 

Div. 6-612.42-Mll 

34. Transducer Research and Production at the New London 
Laboratory, William B. Snow, James W. Follin, Jr., 
Wilbur T. Harris, NDRC 6.1-.srl 128-2212, Report 
G12 1418, NS-113, CUDWR-NLL, May 2.5, 194.5. 

Div. 6-612.1-MS 

35. Magnetic Materials for Magnetostriction Microphones 

(Bell I^aboratories Technical Memorandum), JI. J. 
Williams, R. M. Bozorth, Re|iort 37063, BTL, Jidy 7, 
1942. Div. 6-612.4 Ml 

36. Magneiic Materials for Magnetostriction Microphones and 
Projectors, H. J. Williams, E. A. Nesbitt, M. Goertz, 
Reports 27063-4 and 24714-1, BTL, Mar. 22, 1944. 

Div. 6-612.4-M6 

37. The Magnetostriction, Young’s Modulus and Damping of 
68 Permalloy as Dependent on Magnetization and Heat 
Treatment, H. J. Williams, R. M. Bozorth, H. Christen- 
•sen. Monograph B-1303, BTIj. Div. 6-612.42-M12 

38. Case Report 4399.1, Research I>aboratory, International 
Nickel Co. 

39. “Ferromagnetismus und Phasengestaltung im Zweistoff- 
syslem Nickel Mangan,” Seiji Kaya, Kussman, 
Zeitschrift fur Physik, Vol. 72, 1931, pp. 293-309. 

40. Fairlie Magnetostriction Report, F. D. Smith, HUSIj File 
B[ritish 10], 1931. 

41. “Notes on Electricity and Magnetism,” Ivord Rayleigh, 
Sec. R. S., The London, Edinburgh and Dublin Philosophi¬ 
cal Magazine and Journal of Science, Ser. 5, Vol. 23, 
March 1887, i)p. 225-245. 

42. “Magnetic Measurements at I^ow Flux Densities Using 
the .Alternating Current Bridge,” Victor E. I-egg, Bell 
System Technical Journal, Vol. XV, 1936, pp. 39-62. 

43. Magnetische und Electrische Eigenshaften des Eisens und 
Seiner Legierungen, O. V. .\uer, 1938. 

44. “Die Kobaltecke des Systems Eisens-Kobalt-Vanadin,” 
Werner Koester, Karl Lang, Zeitschrift fur Metallkunde, 
Vol. 30, 1938, pp. 350-352. 

45. Metals Handbook, American Institute of Mining En¬ 
gineers, 1939, p. 1664. 

46. Die Magnetisierung bei Schwachen Feldern, a die Rayleigh 
Schleife, Wechselstromuntersuchungen im Rayleigh Ge- 
beit, R. Becker, W. Doering, Julius Springer, Berlin, 
Germany, 1939 (Edwards Bros. Inc., .Ann .Arbor, Mich., 
1943) pp. 218-228. 

47. “Demagnetizing Factor of Rods,” R. M. Bozorth, 
D. M. Chapin, Journal of Applied Physics, Vol. 13, 1942, 
pp. 320-326. 

48. “On the Magnetostriction of Iron-Cobalt .Alloys,” Yosio 
Ma-siyama, The Science Reports of the Tohoku Imperial 
University, Tohoku Imijerial University, Sendai, Japan, 
Ser. 1, Vol 21, 1932, pp. 394-410. 


Chapter 5 


1. Directivity of Radiation, O. Hugo Schuck and Others 
(October 1941 to March 1942), M 01.21-1, HUSL, 
March 1942. Div. 6-612.21-Ml 


2. Directivity Patterns of Sound Sources, W. O. Pennell, 
Malcolm H. Hebb, Harvey A. Brooks and Others, 
NDRC C4-sr287-089, HUSL, Ai)r. 29, 1942. 

Div. 6-551-M2 


CONFIDENTIAL 




BIBLIOGRAPHY 


459 


3. Absolute Efficiency of Projectors and Hydrophones, Egin- 
hard Diotze, NDRC C4-sr20-150, USRL, Aug. 3, 1942. 

Div. 6-5.51-M3 

4. The Absolute Efficiency of a Device Used as a Projector 

and as a Hydrophone, Eginhard Dietze, NDRC C4-.sr20- 
197, U.SRL, Aug. 18, 1942. Div. 6-551-M4 

5. Program for Studies of Delay Method of Making Toroidal 
Hydrophone Uni-Directive, .1. Warren Hortun, Report 
G12 '3769, CUDWR-NLL, Aug. 21, 1942. 

Div. 6-612.21-M4 

6. Angular Characteristics of the WEA-1 Used as a Hydro¬ 
phone (Memorandum for File), Edward Gerjuoy, Re¬ 
port G13/176, CUDWR-NLL, Mar. 2, 1943. 

Div. 6-556.1-M9 

7. Directivity Considerations for Echo Ranging Projectors, 
Eginhard Dietze, Ijcslie L. Foldy, NDRC 6.1-sr20-617, 
Navy Project NS-139, USRL, Apr. 30, 1943. 

Div. 6-551-M9 

8. Magnetostrictive Transducers, Malcolm 11. Ilebb, Harvey 
A. Brooks, NDRC 6.1-sr287-898, HUSL, .June 22, 1943. 

Div. 6-612.1-M2 

9. Theoretical Directivity Characteristics for Line Hydro¬ 

phones, Wilbur T. Harris, Report G12/4.50, CUDWR- 
NLL, Aug. 26, 1943. Div. 6-612.21-M6 

10. Bearing Accuracy of 3-ft, 2-ft, and 1-ft Straight Magneto¬ 

striction Hydrophones (Memorandum for File), Ralph 
C. Maninger, Report D17/.543, CUDWR-NLL, Oct. 9, 
1943. Div. 6-612.62-M17 

11. Pattern Requirements for Sonar Transducer, Malcolm H. 
Hebb, M 02.45.70-38, HUSL, Oct. 15, 1943. 

Div. 6-612.21-M7 

12. Shifted Lobe and SLC Patterns of a Phase and Shaded- 

Square Transducer, Gerald 1. Harrison, M 01.21-41, 
HUSL, Nov. 19, 1943. Div. 6-612.21-M8 

13. Advantages of Increased Hydrophone Length to Sonic 

Listening, Arthur Ij. Thuras, Report G12/631, CUDWR- 
NLL, Dec. 6, 1943. Div. 6-612.21-M9 

14. Performance of the JP Baffie at Supersonic Frequencies, 

Edward Gerjuoy, Report G12/643, CUDWR-NI^L, 
Dec. 11, 1943. ' Div. 6-612.62-M19 

15. Theoretical Patterns for Circular Radiators, Nelson M. 
Blachman, M 01.21-44, HUSL, Dec. 30, 1943. 

Div. 6-612.21-MlO 

16. Acoustic Radiation from Sources at the Top of a Semi- 
Infinite Cylinder, .J. K. L. MacDonald, AMP, NDRC, 
M 01.21-45, HUSL, .Jan. 5, 1944. 

17. Directivity Ratios for Circular Pistons, Nelson M. Blach¬ 
man, M 01.21-50, HUSL, Feb. 3, 1944. 

Div. 6-612.21-Mll 

18. Delay Network to Obtain Front-to-Back Discrimination, 
James W. Follin, Jr., Report G12/743, NS-129, 
CUDWR-NLL, Feb. 11, 1944. Div. 6-612.21-M12 

19. The Vertical Pattern of a Split Sonar Element, Malcolm 

H. Hebb, Nelson M. Blachman, M 01.21-56, HL'SL, 

Mar. 1, 1944. Div. 6-612.21-M13 

20. Circular Transducer Patterns, Gerald 1. Harrison, 
M 01.21-62, HUSL, Apr. 7, 1944. Div. 6-612.21-M14 

21. Patterns of Radiators in Pressure-Release Baffies, Gerald 

I. Harri.son, M 01.21-65, HUSL, Apr. 12, 1944. 

Div. 6-612.21-M15 


22. Single Element Pattern of Cylindrical Transducer, Gei-ald 
1. Harrison, M 01.21-68, HUSL, Apr. 28, 1944. 

Div. 6-612.21-M16 

23. Appearance of 90° Minor Lobes in Scanning Sonar Trans¬ 
ducer Patterns, Thomas P. Merritt, Francis P. Bundy, 
M 02.45.7-90, HUSL, May 13, 1944. Div. 6-632.61-M2 

24. Elimination of Side-Lobe Interference in the RLI, Part I 
Theoretic (Memorandum for File), James W. Follin, Jr., 
Report G12 '947, CUDWR-NLL, June 8, 1944. 

Div. 6-612.21-M17 

25. Comparative Tests on 3-ft, 4-ft, and 5-ft Hydrophones, 

Ralph C. Maninger, Report P33/949, CUDWR-NLL, 
June 12, 1944. Div. 6-612.62-M27 

26. Radiation Impedance and Equivalent Circuits, Malcolm 
H. Hebb, Gerald 1. Harrison, Nelson M. Blachman, 
M 01.21-84, HUSL, June 17, 1944. Div. 6-612.32-M2 

27. Directivity Ratio of Transducers, Gerald 1. Harrison, 
M 01.21-88, HUSL, Aug. 21, 1944. Div. 6-612.21-M18 

28. Shaded Line Sources, Gerald 1. Harrison, M 01.21-91, 

HUSL, Sept. 7, 1944. Div. 6-612.21-M19 

29. Directivity Ratio of Long Sources, Gerald I. Harrison, 
M 01.21-96, HUSL, Oct. 9, 1944. Div. 6-632.0-M19 

30. Sound Beam Patterns in Sea Water, NDRC 6.1-sr31-1730, 

WHOI, Oct. 10, 1944. Div. 6-510.11-M9 

31. Directivity Ratios, Malcolm H. Hebb, M 01.21-103, 

HUSL, Nov. 2, 1944. Div. 6-612.21-M20 

32. Directivity at Low Sonic Frequencies (Memorandum for 
File), Walter F. Graham, Ralph C. Maninger, Report 
P33/1067, CUDWR-NLL, Nov. 8, 1944. 

Div. 6-612.21-M21 

33. Pattern of a Sector of a Cylinder, Gerald 1. Harrison, 
M 01.21-107, HUSL, Nov. 14, 1944. Div. 6-612.21-M22 

34. Improvement in Submarine Sonic Listening and Bearing 
Accuracy, Arthur L. Thuras, Report G12/1251, NS-102, 
CUDWR-NLL, Nov. 21, 1944. Div. 6-612.21-M23 

35. Single Element Scanning Sonar Patterns, Gerald 1. 
Harrison, M 02.45.7-143, HUSL, Nov. 24, 1944. 

Div. 6-632.61-M3 

36. Directivity Patterns of a Delobed Hydrophone for Various 

Octave Bands (Memorandum for File), Jordan J. Mark¬ 
ham, Report G12/1254, NS-102, CUDWR-NLL, Nov. 
27, 1944. Div. 6-612.21-M24 

37. A Statistical Theory of Errors in Pattern Formation, 
Gerald 1. Harrison, M 02.45.1-21, HUSI^, Dec. 28, 1944. 

Div. 6-612.21-M25 

38. Theoretical Formulae of Hydrophone Patterns Integrated 
over a Band of Frequencies, LeRoy A. Woodward, 
Report G12/1301, NS-102, CUDWR-NLL, Jan. 8, 1945. 

Div. 6-612.21-M27 

39. Theoretical Scanning Sonar Patterns, Gerald 1. Harrison, 
M 02.45.1-22, HUSL, Jan. 19, 1945. Div. 6-632.61-M4 

40. Pattern of a 270° Sector (Corrected), Gerald 1. Harrison, 
M 01.21-113, HUSL, Jan. 26, 1945. 

Div. 6-612.21-M28 

41. Scattering and Radiation from Circular Cylinders and 

Spheres, Tables of Amplitudes and Phase Angles, Arnold 
N. Lowan, Phillip M. Morse, H. Feshbach, Marvin Lax, 
NDRC 6.1-srl046-2032, AMP Report 62.1 R, MIT and 
AMP, February 1945. Div. 6-612.21-M29 


CONFIDENTIAL 





460 


biblio(;raphv 


42. Pattern of 270° and 00° Sectors {Really Correct), Gerald 

I. Harrison, M 01.21-115, liUSL, Feb. 26, 1945. 

Div. 6-612.21-M30 

43. Total Attenuation Patterns, Gerald I. Harrison, M 01.21- 

119, HFSL, Mar. 24, 1945. Div. 6-612.21-M32 

44. Transmission Pattern for Constant Echo Strength, Gerald 
I. Harrison, M 01.75-15, HFSL, Mar. 26, 1945. 

Div. 6-612.21-M33 

45. Recommendations on Attenuation and Lag Lines for the 

Sangamo XQHA System, Gerald I. Harrison, M 01.21- 
126, HFSL, Apr. 2, 1945. Div. 6-632.221-M4 

46. Design B for Scanning Sonar XQHA, Gerald L Harrison, 
M 02.45.1-26, HFSL, Apr. 14, 1945. Div. 6-632.221-M6 

47. Scanning Sonar Pattern Formation, Gerald I. Harrison, 
M 02.45.1-27, HFSI., .4pr. 14, 1945. Div. 6-632.61-M6 

48. Theoretical Scanning Sonar Patterns, Gerald I. Harri.son, 
M 02.45.1-29, HFSL, Apr. 16, 1945. Div. 6-632.61-M7 

49. Further Subdivision of Scanning Rotor to Achieve More 

I’niform Rotation of Beam, Malcolm H. Hehb, M 02.45.1- 
31, HFSL, .\pr. 19, 1945. Div. 6-632.61-M8 

50. Transducer Research and Production at the New London 
Laboratory, William B. Snow, James W. P'ollin, Jr., 
Wilbur T. Harris, XDRC 6.1-srl 128-2212, Report 
G12 1418, CFDWR-XLL, May 25, 1945. 

Div. 6-612.1-M8 

51. Advance Notice of Report on Directivity Patterns, HFSL. 

Div. 6-612.21-M34 

52. Submarine Detection, Directivity Indications, Harry 

Xyquist, BTL, Oct. 11, 1941. Div. 6-560.2-Ml 

53. (hi the theory of the directionality patterns of continuous 
source distributions on a plane surface, R. Clark Jones, 
Report MM-42-110-5, BTL, Mar. 10, 1942. 

Div. 6-612.21-M2 


54. Subaqueous IJstening, Directivity of a Pair of Rings, 
Harry Xyquist, C4-XDRC-0f)4, BTL, Apr. 2, 1942. 

Div. 6-560.2-M2 

55. Directivity with Two Microphones, Harry Xyquist, 
C4-XDRC-071, BTL, June 12, 1942. Div. 6-560.2-M4 

56. Directivity of Sound in Water, Elementary Arrays 

(Memorandum), Harry Xyquist, C4-XDRC-072, BTL, 
June 24, 1942. Div. 6-612.21-M3 

57. Directivity with Two Microphones, Addition vs Multi¬ 

plication of Outputs, Harry Xyquist, C4-X’DRC-073, 
BTL, July 1, 1942. Div. 6-560.2-M5 

58. Diffraction around a Cylinder, W. H. Wi.se, C4-XDRC- 

117, BTL, July 15, 1942. Div. 6-530.1-M2 

59. “Fber die Riehtweirkung von Schallstrahlern,” H. 
Stenzel, Elektrische Nachrichlen-Technik, Vol. 4, 1927, 
p. 239. 

60. “Reciprocity in kiJectromagnetic, Mechanical, .\cousti- 
cal, and Interconnected Systems,” Stuart Ballantine, 
Proceedings of the Institute of Radio Engineers, Vol. 17, 
.lime 1929, pp. 929-951. 

()1. .4 Short Table of Integrals, B. O. Pierce, Ginn and Co., 
Boston, Mass., 192t), pp. 116-119. 

62. Vibration and Sound, P. M. Morse, McGraw-Hill Book 
Co., Inc., Xew York, X. Y., 1936, p. 246. 

63. Tables of Functions, Eugen Jalmke, Fritz Emde, B. G. 
Teubner, Leipzig and Berlin, Germany, 1938 (Dover 
Publications, X'ew York, X. Y., 1943), j). 24. 

63a. Ibid., p. 29. 

63b. Ibid., p. 219. 

64. Theory of Bessel Functions, G. X. Watson, Macmillan 
Co., Xew York, X. Y., 1944, j). 328. 


I’.hapter 6 


1. The Tubular Magnetostriction Microphone, .Arthur L. 

Thuras, Rejjort G4 1937, CFDWR-XLL, Mar. 17, 
1942. Div. 6-554.2-Ml 

2. Listening Tests on Thuras Doughnut Hydrophone, Donald 

P. Loye, Report G12 2679, CFDWR-XLL, Ajir. 30, 
1942. Div. 6-612.62-Ml 

3. Disclosure of Invention, Magnetostriction Microphone, 

.Arthur L. Thuras, Report G5 2625, CL'DWR-XLL, 
May 2, 1942. Div. 6-612.62-M2 

4. Present Status of the Development of Line Microphones, 

Warren Horton, Report G12 3129, CFDWR-XLL, 
June 13, 1942. Div. 6-612.62-M3 

5. Development of the Directional Voice-Frequency Toroidal 
Magnetostriction Hydrophone (Progress Report), Arthur 
L. Thuras, XDRC C4-sr20-214, OSRD 775, Report 
G5s 3413, CFDWR-XLL, July 1, 1942. 

Div. 6-554.2-M3 

6. Laminated Magnetostriction Tubes, Malcolm H. Hebb, 
M 01.213-7.1, HFSL, Xov. 7, 1942. Div. 6-612.63-Ml 

7. Thuras Type Microphones at 100 kc and 1 me, Malcolm 
H. Hebb, M 01.213-9.1, HFSL, Dec. 1, 1942. 

Div. 6-612.62-M4 


8. Tubular Magnetostriction Hydrophone with Cylindrical 

Internal Coil, Hector F. Bernier, Report G27 131, 
CFDWR-XLL, Dec. 18, 1942. Div. 6-612.62-M5 

9. Residual Magnetism in an I’nannealed Nickel B-Type 

Hydrophone, Paul E. Sabine, M 01.213-28, Hl'SL, .Ian. 
28,1943. Div. 6-612.41-Ml 

10. Comparison of Piezoelectric and Magnetostriction Hydro¬ 

phones for Sonic Listening (Memorandum), James W. 
Follin, Jr., XDRC 6.1-sr20-653, Report G27 130, 
CFDWR-XLL, Mar. 21, 1943. Div. 6-554-M19 

11. Development of Magnetostriction Hydrophones, July 1, 

J94.2-Apr. 1, 194 s (Progress Report), .Arthur L. Thuras, 
XDRC 6.1-sr20-639, Report G12, 158, CFDWR-XLL 
[1943]. Div. 6-612.62-M6 

12. Notes and Observations from Lecture by Arthur L. Thuras 

at New London, March 24, Francis P. Bundy, 

M 01.213-34, HFSL, Apr. 3, 1943. Div. 6-612.62-M7 

13. Information on B-27A Nos. 1 and 2, 39-kc Ay[ckel] Ring 

Stack Transducer, Francis P. Bundy, M 01.223-24, 
HFSL, May 12, 1943. Div. 6-612.61-Ml 


COXFIDENTIAI 



BIBLIOGRAPHY 


161 


14. Tests on Small Straight Magnetostriction Hydrophones 
Constructed with Electrofornicd Shells (Memorandum for 
File), Robert R. MacLaughlin, Reirort DIG 315, 
CUDWR-NLL, May 18, 1943. Div. G-612.G2-M8 

15. Type Tests on ANfCRT-l Units, Second Group (Memo¬ 
randum for File), Henry M. Jasper, Jr., Report DIG/- 
37G, XS-IOG, CFDWR-NLL, May 19, 1943. 

Div. G-G12.62-M9 

IG. Characteristics of B-19B SGM Transducer, Francis P. 
Bundy, M 02.331.7-24, Hl'SL, June 7, 1943. 

Div. G-G12.G11-M1 

17. Straight Toroidatly Wound Magnetostriction Hydrophone, 

TMS-dS, James W. Follin, Jr., Report G12 '394, 
CFDWR-NLL, June 8, 1943. Div. G-G12.G2-M1() 

18. Portable SGM Transducers, Francis P. Bundy, M 02.331.- 

7-2G, HUSL, June 10, 1943. Div. G-612.G11-M2 

19. Sensitivity of B-lUB SGM Transducer, Francis P. Bundy, 
M 02.331.7-28, HFSL, June 15, 1943. 

Div. G-612.G11-M3 

20. Orlando Calibration of Proposed Mark 24 Mine Micro¬ 

phone, Lyman N. Miller, M Gl.2165-319, HUSL, June 
17, 1943. Div. 6-612.55-M3 

21. Tests on Small Hydrophones, for ERSB, Submitted by 
Aircraft Radio Laboratory (Memorandum for File), 
Robert R. MacLaughlin, Report DIG,'433, NS-IOG, 
CUDWR-NLL, July 16, 1943. Div. G-G12.62-M11 

22. Reduction of Eddy Currents in Magnetostrictive Tubes, 
Malcolm H. Hebb, M 01.213-62, HUSL, July 24, 1943. 

Div. 6-G12.8-M4 

23. Suggestions on Procedures for Testing SGM Transducers 
as They Proceed through the Production Line, Francis P. 
Bundy, M 02.331.37-9, HUSL, July 29, 1943. 

Div. 6-612.611-M4 

24. Proposed Changes in DIB Mark IV-E Hydrophones 
(Memorandum for File), Robert R. MacLaughlin, Report 

D16 467, CUDWR-NLL, Aug. 3, 1943. 

Div. 6-612.62-M13 

25. Tests on Hydrophones with Shells Specially Heat Treated 
by C. G. Conn, Ltd., Robert R. MacLaughlin, Report 
DIG, 473, NS-102, CUDWR-NLL, Aug. 11, 1943. 

Div. 6-612.41-M5 

26. Criticism of MOX and MKX Magnetostrictive Hydro¬ 

phones, Lyman N. Miller, M 61.036-372, HUSL, Aug. 
19, 1943. Div. 6-612.63-M3 

27. Theoretical Directivity Characteristics for Line Hydro¬ 

phones, Wilbur T. Harris, Report G12 450, CUDWR- 
NLL, Aug. 26, 1943. Div. 6-612.21-M6 

28. Bell Telephone Laboratories' Magnetostrictive Brainstorm, 

Type MKX, Frederick V. Hunt, M 01.223-42, HUSL, 
Aug. 30, 1943. Div. 6-612.63-M4 

29. Tests on Twenty ERSB Hydrophones (Memorandum for 
File), Edward Gerjuoy, Robert R. MacLaughlin, Re¬ 
port D16 496, CUDWR-NLL, Sept. 3, 1943. 

Div. 6-612.62-M14 

30. Heat Treatment of Nickel, Robert R. MacLaughlin, Re¬ 
port G12 530, CUDWR-NLL, Sej)!. 14, 1943. 

Div. 6-612.41-M7 

31. Tests of the First of Harvey Radio Laboratories’ B-19B 

Transducer, Francis P. Bundy, M 02.331.37-27, HUSL, 
Sept. 28, 1943. Div. 6-612.611-M5 


32. Methods of Constructing Layer-Built Magnetostrictive 
Tubes to Be I'sed as Radial Oscillators, Francis P. Bundy, 
M 01.213-85, HUSL, Sept. 30, 1943. Div. 6-612.62-M15 

33. Tests on Ten Series C ERSB Hydrophones (Memoran¬ 
dum), Edward Gerjuoy, Robert R. MacLaughlin, Re- 
jrort D16/536, CUDWR-NLL, Oct. 1, 1943. 

Div. 6-612.62-M16 

34. Notes on Painting JP-1 Hydrophones, Frank M. Goyan, 
Report D24 '539, CUDWR-NLL, Oct. 6, 1943. 

Div. 6-612.44-M4 

35. Performance Tests on SGM Monitor Model 50, Serial 
No. 2, with B-19B No. 26 Hydrophone, Paul E. Sabine, 
M 02.331.7-35, HUSL, Oct. 7, 1943. Div. 6-612.611-M6 

36. Results of Tests on Cyclewelded 20 kc Ring Stack, Franci.s 
P. Bundy, M 01.213-96, HUSL, Oct. 14, 1943. 

Div. 6-612.61-M2 

37. Measurements of Three-Foot Straight Wood Core Hydro¬ 
phone, D54B-6 and D54B-7, Edward Gerjuoy, Frank M. 
Goyan, Report G12'547, CUDWR-NLL, Oct. 15, 1943. 

Div. 6-612.62-M18 

38. Measurements of Toroidatly Wound Magneto¬ 

striction Hydrophones, Evaluation of Annealing of Nickel, 
Edward Gerjouy, Wilbur T. Harris, Report D16 '555, 
CUDWR-NLL, Oct. 19, 1943. Div. 6-612.41-M8 

39. Measurements of o-Inch Toroidatly Wound Magnetostric¬ 

tion Hydrophones, Edward Gerjuoy, Report D16;557, 
CUDWR-NLL, Oct. 20, 1943. Div. 6-612.55-M5 

40. Tests of the Large 4-Begment 20-kc Ring Stack, Francis P. 
Bundy, M 01.213-98, HUSL, Oct. 21, 1943. 

Div. 6-612.61-M3 

41. VIR Teardrop Transducer for Installed Sound Gear 

Monitor, Francis P. Bundy, M 02.331-83, HUSL, Oct. 
22,1943. Div. 6-612.611-M7 

42. Permanent Magnet Polarization of Laminated Ring 

Stacks, Franci.s P. Bundy, M 01.213-100, HUSL, Oct. 
25, 1943. Div. 6-612.1-M6 

43. Sea Tests of JP-1 Hydrophone, A. L. Thuras, Ralph 

C. Maninger, Hector F. Bernier, Report G12/581, 
CUDWR-NLL, Nov. 1, 1943. Div. 6-612.55-M6 

44. Measurements of JP Hydrophones, Edward Gerjuoy, 
Re])ort G12 .597, CUDWR-NLL, Nov. 8, 1943. 

Div. 6-612.55-M7 

45. Performance of the 5”, 20-kc, Oxide Annealed Ring- 

Stacks, 20 ARS-2, Francis P. Bundy, M 01.213-110, 
HUSL, Nov. 8, 1943. Div. 6-612.41-MlO 

46. Performance of the 5" 20-kc Hardened Nickel Ring Slack, 
20 HRS-1, Jack C. Cotton, Francis P. Bundy, M 01.- 
213-112, HUSJ., Nov. 17, 1943. Div. 6-612.41-Mll 

47. Measurements on 20-kc Ring Stack, James W. Follin, 
Jr., M 01.213-115, HUSL, Nov. 20, 1943. 

Div. 6-612.61-M4 

48. Performance of the 60 kc Ring Stacks H-9 and H-W, 
Individually and in Combination, Jack C. Cotton, Fraticis 
P. Bundy, M 01.213-114, HUSL, Nov. 23, 1943. 

Div. 6-612.61-M5 

49. JP-1 Hydrophone Vibration Measurement, Arthur L. 
Thuras, Hector F. Bernier, Report G12/620, NS-113, 
CUDWR-NLL, Nov. 23, 1943. Div. 6-612.55-M8 

50. Ring Stacks, Response of Arrays of, Frederick V. Hunt, 
M 01.213-119, HUSL, Nov. 29, 1943. Div. 6-612.61-M6 


CONFIDENTIAL 




462 


biblio(;kaphv 


51. Performance of the 60-ARS-l and -2 Ring Slacks, .Jack 

C. Cotton, Francis P. Bundy, M 01.213-121, IIUSL, 
Dec. 1, 1943. Div. 6-612.61-M7 

52. Hard Nickel Laminated Transducers as Powerful Under¬ 
water Sound Projectors, Francis P. Bundy, Roland E. 
Mueser, M 01.213-123, IIUSL, Dec. 3, 1943. 

Div. 0-G12.41-M12 

53. Advantages of Increased Hydrophone Length to Sonic 

Listening, .Arthur L. Thuras, Report G12/631, XS-113, 
CUDWR-XLL, Dec. 6, 1943. Div. 6-612.21-M9 

54. Performance of the JP Baffle at Supersonic Frequencies, 

Edward Gerjuoy, Report G12;643, CUDWR-XLL, 
Dec. 11, 1943. Div. 6-612.62-M19 

55. Measurements of Two JP-1 Hydrophones ivith NL-105 

No. 4 Amplifier, Edward Gerjuoy, Report G12 064, 
CUDWR-XLL, Dec. 27, 1943. Div. 0-612.55-M9 

56. Improved Preamplifier Mounting for 0.41’ S. L. Meter 

Hydrophone (Memorandum for File), Garland W. 
.Archer, Report P35 679, X"0-163, Cin)WR-XLL, .Ian. 
11, 1944. Div. 6-612.62-M20 

57. Measurements of Two-Section Three-Foot Hydrophones, 

Edward Gerjuoy, Report G12/683, CUDWR-XLL, 
•Ian. 11, 1944. Div. 6-612.55-MlO 

58. Data on B-19B Hydrophones, Paul E. Sabine, M 01.213- 

136, IIUSL, .Ian. 14, 1944. Div. 6-612.611-M8 

59. The Complete Magnetizing of a 3-Foot Toroidatly Wound 

.Magnetostriction Hydrophone, Wilbur T. Harris, Edward 
Gerjuoy, Rei)()rt G12 691, XS-139, CUDWR-XLL, 
Jan. 14, 1944. Div. 6 t612.62-M21 

60. Performance Characteristics of a Plastic-Covered Toroidally 

lUoand Hydrophone and Baffle Assembly, Wilbur T. 
Harris, Report G12/708, XS-139, CUDWR-XLL, Jan. 
19, 1944. Div. 6-612.44-M6 

61. The B-19G, No. 1 Transducer, G. W. Renner, M 01.213- 

139, IIUSL, Jan. 24, 1944. Div. 6-612.612-Ml 

62. Installed SGM Transducer, B-19D, No. 4 in VIR Tear¬ 

drop Shell, Francis P. Bundy, Jack C. Cottoti, M 02.331- 
105, IIUSL, Jan. 28, 1944. Div. 6-612.612-M2 

63. Tests on 22 B-19B Hydrophones .Made by Harvey Radio 

Laboratories, Paul E. Sabine, M 02.331.37-44, HUSL, 
.Jan. 29, 1944. Div. 6-612.611-M9 

64. The Complete Magnetization of the JP-1 Hydrophone 

(Memorandum for File), Edward Gerjuoy, Report 
D24 G12 727, XS-113 and XS-139, CUDWR-XLL, 
Jan. 31, 1944. Div. 6-612.55-Mll 

65. Effect of Depth and Depth Charges on a B-19B Hydro¬ 

phone, Paul E. Sabine, M 01.213-151, HUSL, Feb. 15, 
1944. Div. 6-612.611-M10 

66. Monitor Transducer Failures, Fred H. Smith, M 02.331- 

116, HUSL, Feb. 15, 1944. Div. 6-612.611-Mll 

67. Special Hydrophones for Range and Bearing Studies, 

Wilbur T. Harris, Report G12/746, XS-139, CUDWR- 

XLL, Feb. 15, 1944. Div. 6-612.55-M12 

68. Construction and Performance of Echo-Repeater Pair, 

1" Hard Nickel and 2" Annealed Nickel Ring Stacks, Jack 
C. Cotton, Francis P. Bundj’, M 91.236-81, HUSL, 

Feb. 17, 1944. Div. 6-612.41-M14 

69. Methods of Obtaining Band-Pass Characteristics with 
Magnetostriction Transducers, James W. kMllin, Jr., 
M 01.213-155, HUSL, Feb. 17, 1944. 

Div. 6-612.34-M2 


70. The B-19H Transducers, .1. R. Reitz, M 01.223-74, 

HUSL, Feb. 21, 1944. Div. 6-612.613-Ml 

71. Retest of 6 B-19B Hydrophones from Harvey Radio after 

Reannealing the Shells, Paul Pi. Sabine, M 02.331.37-55, 
HUSL, Feb. 24, 1944. Div. 6-612.41-M15 

72. .Annealing of JP-1 Straight Wood Core Hydrophone, 
Hector PA Bernier, Report G12, 753, XS-139 and XS-113, 
CUDWR-XLL, Feb. 26, 1944. Div. 6-612.41-xM 16 

73. Field and Frequency Response Sheet for B-19B, No. IS 
Standard, Simplified Conversion Procedure, Jack C. 
Cotton, M 01.213-165, HUSL, Feb. 29, 1944. 

Div. 6-612.611-M12 

74. Plastic Molding Materials for Transducers as Developed 

at New London Laboratory, P'rancis P. Bundy, M 01.- 
223-81, HUSL, Mar. 6, 1944. Div. 6-612.44-M7 

75. Temperature Variation in Sensitivity of B-19B Hydro¬ 

phones, Paul FA Sabine, M 02-331.37-.58, HUSL, Mar. 6, 
1944. Div. 6-612.611-M13 

76. Two Thimble Hydrophones, Wilbur T. Harri.s, Report 
G12 779, XS-102, CUDWR-XLL, Mar. 6, 1944. 

Div. 6-612.6-Ml 

77. Tests on Lucite-Impregnated 60-Kc Ring Stacks, Jack C. 

Cotton, P’rancis lA Bundy, M 01.213-174, HUSL, 
Mar. 11, 1944. Div. 6-612.61-M8 

78. Depth Charge Tests on Hydrophones, Effect of .Annealing 

on Performance (Memorandum for P’ile), Wilbur T. 
Harris, Phillip B. Pldwards, Robert R. MacLaughlin, 
Report G12 7.54, XS-139, CUDWR-XLL, Mar. 14, 
1944. Div. 6-612.55-M13 

79. .4 Comparison of Some Possible Materials for Use in JP-1 
Baffles, Wilbur T. Harris, David W. Van I^nnep, 
Robert R. MacLaughlin, Report G12 805, XS-113, 
CUDWR-XLL, Mar. 15, 1944. Div. 6-612.55-M13 

80. Installed SGM Transducer B-19H in VIR Pit Log Strut 

Extension, .1. R. Reitz, M 02.331-138, HUSL, Mar. 16, 
1944. Div. 6-612.613-M2 

81. Effect of Tape Ties upon the Acoustic Functioning of the 

M7/CRT-1 A Hydrophone (Memorandum for File), 
Robert R. MacLaughlin, David W. Van Lennep, Henry 
Suter, Report D16 '798, XS-106, CUDWR-XLL, Mar. 
20, l‘)44. Div. 6-612.62-M22 

82. Effect of Shell Painting upon the Acoustic Functioning 
of the M7 CRT-l A Hydrophone (Memorandum for P’ile), 
Robert R. MacLaughlin, David W. Van Lennep, Re¬ 
port D16 799, XS-106, CUDWR-XLL, Mar. 20, 1944. 

Div. 6-612.51-M8 

83. Permanent Magnet Core Blastphone, .Arthur L. Thuras, 
Report G12 8.53, CUDWR-XLL, .Apr. 6, 1944. 

Div. 6-612.62-M23 

84. General Purpose Nondirectional Sonic Magnetostriction 

Hydrophones, Wilbur T. Harris, David W. Van Lennep, 
Phillip B. Edwards, Report G12 852, CUDWR-XLL, 
.Apr. 10, 1944. Div. 6.-612.62-M24 

85. .4 Permanent Magnet Magnetostriction Hydrophone Con¬ 
struction, Wilbur T. Harris, David W. Van Lennep, 
Report G12 858, CUDWR-XLL, .Apr. 12, 1944. 

Div. 6-612.62-M25 

86. The B-19H Transducers [Memorandum] II, J. R. Reitz, 
M 01.223-186, HUSL, Apr. 13, 1944. Div. 6-612.613-M3 


COXFIDENTI.VL 



KIBLIOGRAPIIY 


463 


87. Effect of Hanxjing eights from the Bottom of Monitor 

Transducers,.]. R. Reitz, M 02.331.7-73, HUSL, Apr. 17, 
1944. Div. 6-612.613-M4 

88. Scroll Slack Transducer, April IS, 1944, John U. Lane, 
M 01.213-189, HUSL, Apr. 19, 1944. Div. G-612.63-M5 

89. Magnetostriction Beeper Listening Hydrophone, R. W. 
Marsh, M 00.004-077, HUSL, .\pr. 19, 1944. 

Div. 0-012.011-M14 

!)0. Visit to New London, April 19 [1944], Plastic Potting, 
Alan H. Selkcr, M 110.10-128, HUSL, Apr. 20, 1944. 

Div. 0-012.44-M8 

91. Self-Polarized Ring Stacks, Francis P. Bundy, G. W. 
Renner, M 01.213-194, Hl'SL, May 9, 1944. 

Div. 0-012.01-M9 

92. Measurements on Two B-19B Hydrophones to Be Used as 
Secondary Standard for Production Tests on OAX-1 
Monitors by Harvey Radio Corporation, Paul E. Sal)ine, 
M 02.331.37-0'), HUSL, May 11, 1944. 

Div. 0-012.011-M 15 

93. The B-19H Expanded Range Monitor, .1. R. Reitz, 
M 02.331-108, HUSL, May 12, 1944. 

Div. 0-012.013-M5 

94. Tests on Two Plastic-Covered, Three-Foot Straight 
Toroidally Wound Hydrophones, David W. Van Lennep, 
Report G12 '915, NS-139, CUDWR-NLL, May 12, 1944. 

Div. 0-012.44-M9 

95. Effect of Annealing on the Magnetic Properties of Nickel 

Tubing (Memorandum for File), .Arthur L. Thuras, 
James W. Follin, Jr., Report G12/928, CUDWR-XLL, 
May 10, 1944. Div. 0-012.41-M 19 

90. The Hydrophone H-llo, Wilbur T. Harris, David W. 

Van Lennep, Report G12/929, CUDWR-X^LL, May 19, 
1944. Div. 0-012.02-M20 

97. Midget Element Magnetostriction Hydrophones, Wilbur 
T. Harris, Phillip B. Edwards, David W. Van Lennep, 
Report G12 889, CUDWR-XLL, May 23, 1944. 

Div. 6-012.0-M2 

98. Construction and Performance of (lO-kc Echo Repeater 
Transducer, Pair No. 3, Francis P. Bundy, Milton R. 
Carlson, M 91.230-100, HUSL, May 24, 1944. 

Div. 0-012.01-M10 

99. Sensitivity and Pattern Measurements on Five Monitor 
Hydrophones Submitted by Presto Recording Corporation, 
Paul E. Sabine, M 02.331.37-73, HUSL, June 8, 1944. 

Div. 0-012.011-M 10 

100. Elimination of Side-Lobe Interference in the RLl, Part I 
Theoretic (Memorandum for File), James W. Follin, Jr., 
Report G12/947, CUDWR-XLL, June 8, 1944. 

Div. 6-012.21-M17 

101. Comparative Tests on 3-ft, 4-ft, and 5-ft Hydrophones, 

Ralph C. Maninger, Report P33/949, CUDWR-XLL, 
June 12, 1944. Div. 0-012.62-M27 

102. Procedure for Assembly of B-19H Expanded Range 

Monitor Hydrophones, J. R. Reitz, M 02.331.2-59, 
HUSL, June 13, 1944. Div. 0-612.013-MO 

103. The Straight Toroidally Wound Plastic Covered Magneto¬ 

striction Hydrophone (Interim Report), Wilbur T. Harris, 
XDRC 0.1-sr 1128-1573, Report G12 804, CUDWR- 
XLL, June 15, 1944. Div. 6-012.02-M28 

104. Scroll Transducer Project, John D. Lane, M 01.223-102, 

HUSL, June 17, 1944. Div. 0-012.03-M0 


105. Testing of B-19B Transducers at Presto Recording Cor¬ 
poration, Francis P. Bundy, M 02.331.37-79, HUSL, 
June 28, 1944. Div. 0-012.011-M17 

100. Tubular MS Transducer Consisting of Helix of Fine 
Nickel Tubing, Xelson M. Blachman, Malcolm H. Hebb, 
M 01.223-104, HUSL, July 1, 1944. Div. 0-012.02-M29 

107. Elimination of Longitudinal Resonance in the Straight 

Magnetostriction Hydrophone (Memorandum for File), 
Hector F. Bernier, Re])ort G12/1014, CUDWR-XLL, 
July 7, 1944. Div. 0-012.02-M30 

108. Preliminary Specification for the NL-T24 Hydrophone 

of the D,o,o Sonar System, Rei)ort D55/900, CUDWR- 
XLL, July 21, 1944. Div. 0-012.02-M31 

109. Comparison of HUSL and Presto Pattern and Sensitivity 
Measurements on Presto Hydrophones, Paul F). Sabine, 
M 02.331.37-90, HUSL, July 24, 1944. 

Div. 0-012.011-M18 

110. Construction of B-19H Transducers in the Transducer 
Shop, J. R. Reitz, M 02.331.2-03, HUSL, .Aug. 1, 1944. 

Div. 0-012.013-M7 

111. Use of B-19H Hydrophones as Projectors, b'rederick 
Hunt, M 02.331.7-89, HUSL, Aug. 9, 1944. 

Div. 0-012.013-M10 

112. Recalibration of B-19F Hydrophone, Paul E. Sabine, 
M 01.213-219, HUSL, Aug. 11, 1944. Div. 0-012.012-M3 

113. The Modified Baffle for Topside Straight Hydrophones 
(Memorandum for File), .James W. Follin, Jr., Report 
G12 1010, CUDWR-XLL, Aug. 12, 1944. 

Div. 0-012.02-M32 

114. Plastic Casting of Ring-Stack Transducers, G. W. 

Renner, .Alan H. Selker, M 113.5-102, HUSL, .Aug. 29, 
1944. Div. 0-012.01-Mll 

115. Tests on Six NL-130 Hydrophones, David W. Van 

Lennep, Report D.50 1110, XS-238, CUDWR-XLL, 
Sept. 4, 1944. Div. 0-012.02-M33 

110. Measurements on Neiv London Permanent Magnet Hydro¬ 
phone, H-192, Paul E. Sabine, Lou F’ein, M 01.213-223, 
HUSL, Sept. 7, 1944. Div. 0-012.02-M34 

117. A 12"X12" Square Magnetostriction Transducer, Wilbur 
T. Harris, Phillip B. Edwards, David W. Van Lennep, 
Report G12/1171, CUDWR-XLL, Sept. 7, 1944. 

Div. 0-012.8-M15 

118. Five-Foot Split JP-1 Type Permanent Magnet Hydro¬ 
phone, TMS-97, .Arthur L. Thura.s, Report G12/1125, 
CUDWR-XLL, Sept. 14, 1944. Div. 6-012.02-M35 

119. Operation of Topside Sonic Gear on USS Blueback, 

Arthur L. Thuras, Report G12/1127, CUDWR-XLL, 
Sept. 18, 1944. Div. 6-012.02-M30 

120. Magnetostriction Hydrophone Design, .Arthur L. Thuras, 
Report G12/1137, CUDWR-XLL, Sept. 21, 1944. 

Div. 0-012.02-M37 

121. \_The~\ 24.5-kr Spherical Source No. 3, Delivered September 

22, 1944, G. W. Renner, M 01.213-234, HUSL, Sept. 22, 
1944. Div. 0-012.01-M13 

122. Control of Pattern of a Radially Vibrating Transducer, 
Paid E. Sabine, M 01.213-235, HUSL, Sept. 22, 1944. 

Div. 0-012.01-M12 

123. Graphical Evaluation of the Effect on RLI Accuracy of an 
Interfering Signal and a Study of the Relative Merits of the. 
Two-Section, 5-Foot Hydrophone vs the Ten-Section, P.M., 
5-Foot Lobe Reduction Hydrophone from an Interference 


CONFIDENTIAL 



461 


biblio<;rai»hy 


View Point, Frontal Lobe Section Only, Frederick C. 
Reed, Jr., Report D55, 1144, NS-113, Cl’DWR-NLL, 
Sept. 22, 1944. Div. 6-612.5-Ml 

124. High-Pressure H’oter Test on Plastic Cast Transducer, 

G. W . Renner, .\lan H. Selker, M 113.5-166, HUSL, 
Oct. 2, 1944. Div. 6-612.44-M12 

125. Tests of an Improved JP-1 Type. Hydrophone on the CSS 
Blueback (Memorandum for File), Arthur L. Tluiras, 
Report P33, 1161, XS-113, CUDWR-XLL, Oct. 3, 1944. 

Div. 6-612.62-M38 

126. The 2 F Permendur Hydrophones, Wilbur T. Harris, 
David W. Van Lennep, Paul B. Edwards, Report G12- 
1168, XS-102, CUDWR-XLL, Oct. 6, 1944. 

Div. 6-612.8-M16 

127. Funnel Transducers, Wilbur T. Harris, David W. Van 
Lennep, Report G27, 1166, CUDWR-XLL, Oct. 6, 1944. 

Div. 6-612.8-M17 

128. [The] 24.d-kc Spherical Source No. 4, Delivered October 6 , 
1944, G. W. Renner, M 01.213-246, HUSL, Oct. 9, 1944. 

Div. 6-612.61-M14 

129. [The] 6'(Mt 2 VP-1, [Xo.] 1 [RingStack], G. W. Renner, 
M 01.213-263, HUSL, Oct. 24, 1944. Div. 6-612.61-M15 

130. [The] 24.3-kc Spherical Source Transducers, Nos. 5 and 6, 
G. W. Renner, M 01.213-270, HUSL, Oct. 27, 1944. 

Div. 6-612.61-M16 

131. The B-19H Standard Transducers, Production Tests, 
.]. R. Reitz, M 01.213-274, HUSL, Oct. 31, 1944. 

Div. 6-612.613-Mll 

132. Acoustical Measurements on B-19B, No. 12S, Paid E. 
Sabine, M 01.213-275, HUSL, Oct. 31, 1944. 

Div. 6-612.611-M21 

133. Tests on Thin-Walled 2 U Permendur 60-kc Bing Stack, 
Francis P. Bundy, M 01.213-278, Hl^SL, Xov. 2, 1944. 

Div. 6-612.61-M18 

134. [T/ie] 26-kc Projectors for Aide de Camp, G. W. Renner, 
M 02.45-228, HUSL, Xov. 2, 1944. Div. 6-612.61-M17 

135. Directivity at Low Sonic Frequencies (Memorandum for 
File), Walter F. Graham, Ralph C. Maninger, Report 
P33 1067, CUDWR-XLL, Xov. 8, 1944. 

Div. 6-612.21-M21 

136. Test Equipment and Methods for Relative Permeability 
Measurements on Nickel Tubing (Memorandum for File), 
Robert R. MacLaughlin, Report G12''1230, XS-102, 
CUDWR-XLL, Xov. 10, 1944. Div. 6-612.8-M18 

137. [The] 60-kc 2 VP-1, [Xo.] 2 [Ring Stack], G. W. 
Renner, M 01.213-281, HUSL, Xov. 16, 1944. 

Div. 6-612.61-M19 

138. Tests on Two COG 51053, JP-1, Hydrophones in NL-109 
Baffles Removed from CSS Sargo and CSS Gabilan, 
David W. Van Lennep, Wilbur T. Harris, Report D24 - 
1243, CUDWR-XLL, Xov. 17, 1944. 

Div. 6-612.62-M39 

139. [The] 60 ARS [Xo.] 10 [Ring Stack], G. W. Renner, 
M 01.213-284, HUSL, Xov. 20, 1944. Div. 6-612.61-M20 

140. Improvement in Submarine Sonic Listening and Bearing 
Accuracy, Arthur L. Thuras, Report G12 1251, XS-102, 
CUDWR-XLL, Xov. 21, 1944. Div. 6-612.21-M23 

141. Directivity Patterns of a Delobed Hydrophone for Various 

Octave Bands (Memorandum for File), Jordan J. Mark¬ 
ham, Report G12, 1254, XS-102, CUDWR-XLL, Xov. 
27, 1944. Div. 6-612.21-M24 


142. The B-19J Hydrophones, J. R. Reitz, M 01.223-120, 

HUSL, Xov. 29, 1944. Div. 6-612.614-Ml 

143. [The] 60-kc 2 UP Spherical Source [Xo.] 1 [Ring Stack], 
G. W. Renner, M 01.213-290, HUSL, Dec. 5, 1944. 

Div. 6-612.61-M21 

144. Sensitivity of B-19K, No. 1, Lou f'ein, M 01.213-293, 

HUSL, Dec. 8, 1944. Div. 6-612.615-M2 

145. Tests on NL-124 Hydrophones .Manufactured by Astatic 
Corporation, David W. \^an Lennep, Wilbur T. Harris, 
Report G12 1284, XS-102, CUDWR-XLI,, Dec. 15, 

1944. Div. 6-612.62-M40 

146. Hydrophone Specification for X-OCP Monitors, J. R. 
Reitz, M 02.331.7-118, HUSL, Dec. 18, 1944. 

Div. 6-612.613-M12 

147. Use of Filament Heater for Soldering and Design of New 
Soldering Jig for B-19H, J. R. Reitz, Alan H. Selker, 
M 110.1-169, HUSL, Dec. 19, 1944. Div. 6-612.613-M 13 

148. -4 Permanent Magnet Magnetostriction Hydrophone Con¬ 

struction {Completion Report), Wilbur T. Harris, XDRC 
6.1-srl 128-1921, Report G12 1248, XS-102, CUDWR- 
XLL, Dec. 20, 1944. Div. 6-612.62-M41 

149. Loic Frequency Thin-Walled 2 UP Ring Stacks, G. W. 
Renner, M 01.213-298, HUSL, Jan. 18, 1945. 

Div. 6-612.61-M22 

150. The B-19K Hydrophone for Low-Frequency Monitoring, 
J. R. Reitz, M 01.223-127, HUSL, Jan. 2f), 1945. 

Div. 6-612.615-M3 

151. [The] 60-Kc 2 VP Spherical Source [Xo.] 3 [Ring Stack], 
G. W. Renner, M 01.213-300, HUSL, Feb. 2, 1945. 

Div. 6-612.61-M23 

152. The JP Overside and Through-the-Hull Directive Sonic 
Listening Equipment for Small Patrol Craft, Russell O. 
Hanson, Edwin E. Teal, OSRD 4744, XDRC 6.1-srll28- 
1928, Report D22 D38 1310, CUDWR-XLL, Feb. 7, 

1945. Div. 6-622.2-M5 

153. An Experimental Streamlined Bafiie for Two Hydro¬ 
phones, Wilbur T. Harris, David W. Van Lennep, Re- 
])ort G12/1327, XS-102, CUDWR-XLL, Feb. 9, 1945. 

Div. 6-612.62-M42 

154. Permanent Magnet Sonic Projectors, Wilbur T. Harris, 
Phillip B. Edwards, David W. Van Lennep, Report G27/- 
1353, XS-102, CUDWR-XLL, Feb. 11, 1945. 

Div. 6-612.62-M43 

155. Pit-Log Strut Hydrophone, Conclusions and Recom¬ 

mendations, J. R. Reitz, M 02.331-209, HUSL, Feb. 21, 
1945. Div. 6-612.013-M14 

156. A New and Fitting Design for NL-T24 and NL-T3() 

Hydrophones, Wilbur T. Harris, Phillip B. Edwards, 
Report G12 '1373, XS-102, CUDWR-XLL, Feb. 24, 
1945. Div. 6-612.62-M44 

157. [The] 24.5-Kc No. 2 U Permendur Spherical Source 
Transducer [Xo.] 7 [Ring Stack], G. W. Renner, 
M 01.213-306, HUSL, Feb. 26, 1945. 

Div. 6-612.61-M24 

158. [The] 24 . 5 -kc 2 UP Spherical Source [Xo.] S [Ring 

Stack], G. W. Renner, M 01.213-310, HUSL, Feb. 28, 
1945. Div. 6-612.61-M25 

159. Tests on Beeper Listening Hydrophones, Paul E. Sabine, 
M 60.264-1160, HUSL, Feb. 28, 1945. 

Div. 6-612.611-M23 


CONFIDENTIAL 



BIBLIOGRAPHY 


165 


160. CTlie] 60 kc 2 VP Spherical Source [No.] 2 [Ring Stack], 
G. W. Renner, M 01.213-316, HUSL, Mar. 21, 1945. 

Div. 6-612.61-M26 

161. The B-tOH Hydrophone Specifications, .1. R. Reitz, 
M 02.331.3-117, HUSL, Apr. 5, 1945. 

Div. 6-612.613-M15 

162. Hiyh-Pressure Test of Three B-19H Hydrophones, .1. R. 
Reitz, M 01.213-320, HUSL, A])!'. 9, 1945. 

Div. 6-612.613-M16 

163. Sound Attenuation in Coating Materials, .Alan H. Selker, 
G. W. Renner, M 01.21-128, HUSL, Apr. 9, 1945. 

Div. 6-612.43-M16 

164. Plastic Cast 2 VP Ring Stack, Projector for 25.5-Kc Use, 
G. W. Renner, M 01.213-323, HUSL, Apr. 10, 1945. 

Div. 6-612.61-M27 

165. Oil Filling of Transducers, .Alan H. Selker, M 01.213-324, 

HUSL, Apr. 10, 1945. Div. 6-612.44-M13 

166. [The] 24.0 kc 2 VP Spherical Source, Nos. 9 and 10 [Ring 

Stacks], G. W. Renner, M 01.213-326, HUSL, Apr. 16, 
1945. Div. 6-612.61-M28 

167. Test on Beeper Listening Hydrophones, Paul E. Sabine, 
M 60.264-1285, HUSL, Apr. 20, 1945. 

Div. 6-612.611-M24 

168. I 'nderwater Sonic Loudspeaker, Arthur L. Thuras, NDRC 

6.1-81-1128-1936, Report G13 1352, XS-182, CUDWR- 
N'LL, Apr. 24, 1945. Div. 6-612.62-M45 

169. Experiment in Alteration of the Baffle of a B-19L Beeper 

Listening Hydrophone, Francis P. Bundy, M 60.264-1317, 
HUSL, May 4, 1945. Div. 6-612.616-Ml 

170. Transducer Construction in the Low-Frequency Self-Con¬ 
tained Echo Repeater, Model II, Milton R. Carlson, 
M 91.236-238, HUSL, May 5, 1945. Div. 6-612.61-M29 

171. High-Pressure Tests on B-19H Hydrophones, Paul E. 
Sabine, M 01.213-330, HUSL, May 9, 1945. 

Div. 6-612.613-M17 

172. The Directional Radio Sono Buoy, NDRC 6.1-srll28- 
2224, Report D34 1200, NS-106 and NS-198, OSRD 
5279, CUDWR-NLL, May 20, 1945. Div. 6-624.2-M7 


173. Results of Tests on Eleven David Bogen OB V Hydrophones, 
J. R. Reitz, M 02.331.7-137, HUSL, May 25, 1945. 

Div. 6-612.613-M18 

174. Transducer Research and Production at the New London 
Laboratory, William B. Snow, James W. Follin, .Jr., 
Wilbur T. Harris, NDRC 6.1-srl 128-2212, Report G12/- 
1418, XS-113, CUDWR-XLL, May 25, 1945. 

Div. 6-612.1-M8 

175. Transducer Research and Production at the New London 
Laboratory, William B. Snow, James W. Follin, Jr., 
Wilbur T. Harris, NDRC 6.1-srl 128-2212, Report G12 /- 
1418, XS-113, CUDWR-XLL, May 2.5, 1945. 

Div. 6-612.1-M8 

176. Some Applications of Organic Plastics and Rubber in 

Underwater Sound Apparatus, .Alan H. Selker, M 113.5- 
191, HUSL, May 26, 1945. Div. 6-612.43-M17 

177. Recent Tests on B-19J Hydrophones, .1. R. Reitz, M 01.- 
223-133, HUSL, June 8, 1945. Div. 6-612.614-M2 

178. The 40 PR No. 1, J. R. Reitz, Roland E. Mueser, M 69.- 

016-29, HUSL, Aug. 14, 1945. Div. 6-612.6-M3 

179. The 40 PR No. 2, Esplanade phone, J. R. Reitz, Roland 
E. Mue.ser, M 69.016-33, HUSL, Aug. 20, 1945. 

Div. 6-612.6-M5 

180. Future Work in the PR Field, J. R. Reitz, Roland E. 
Mue.ser, M 69.016-34, HUSL, Aug. 20, 1945 

Div. 6-612.6-M4 

181. Sound Gear Monitor, Undenvater Sound Portable Test 
Equipment (Completion Report), XDRC 6.1-sr287-2086, 
HUSL, Xov. 1, 1945, i)p. 106-107. Div. 6-641.1-M9 

182. Testing Specification for Toroidal Hydrophone, Report 

D22.6/3615, CUDWR-XLL. Div. 6-612.62-M46 

183. MOX and MKX Magnetostriction Hydrophones [R. L. 
Peek], Report 2210-RLP-MS, BTL, June 10, 1943. 

Div. 6-612.63-M2 

184. Non-Directional Magnetostriction Transducer, W. H. 
Martin, XDRC 6.1-srl097-1328, BTL, Feb. 1, 1945. 

Div. 6-.5.54.2-M18 

185. Task No. 4A, Broad Band Magnetostriction Projector 
(Final Report), U. S. Xavy BuShips, Contract X.X sr- 
26932, BTI., June 25, 1945. 


Chapter 7 


1. Laminated Stack Transducer, O. Hugo Schuck, M 01.- 

22.3-5, HUSL, Sept. 2, 1942. Div. 6-612.71-Ml 

2. Tests Suggested for Midget Asymmetrical Stack, O. Hugo 
Schuck, M 01.213-5, HUSL, Sept. 19, 1942. 

Div. 6-612.716-Ml 

3. Laminated Projectors, Frederick A'. Hunt, M 01.223-7, 

HUSL, Nov. 10, 1942. Div. 6-612.71-M2 

4. Winding for 9X9 Asymmetrical Laminated Stack, 
O. Hugo Schuck, M 01.223-10, HUSL, Dec. 5, 1942. 

Div. 6-612.71-M3 

5. The 9''X9" Tests to Be Made at Barge: Patterns, Fre¬ 
quency Response [and] Absolute Calibration, Robert L. 
Cummerow, M 01.213-27, HUSL, Jan. 21, 1943. 

Div. 6-612.71-M4 

6. Completing of Mark II, 9”X9" Asymmetrical Stack of 

0.005" A^t[ckel] Punchings, Francis P. Bundy, M 01.- 
223-13, HUSL, Jan. 26, 1943. Div. 6-612.71-M5 


7. Classification of Stevephones, Lyman X. Miller, M 01.- 

223-15, HUSL, Feb. 3, 1943. Div. 6-612.716-M2 

8. Efficiency Measurements of the Mark I Hugophone, Paul 
E. Sabine, M 01.213-30, HUSL, Peb. 4, 1943. 

Div. 6-612.71-M6 

9. Properties and Uses of Alnico Magnets, Kenneth X. 

Fromm, PTancis P. Bundy, M 01.213-35, HUSL, Apr. 23, 
1943. Div. 6-612.42-Ml 

10. Information on the Mark I, 9"X9" Asymmetric Laminated 
Stack Hydrophone, Leon W. Camp, P'rancis P. Bundy, 
Paul E. Sabine, M 01.223-25, HUSL, May 29, 1943. 

Div. 6-612.71-M8 

11. The pc Rubber, P’rancis P. Bundy, M 113.50-25, HUSL, 

June 10, 1943. Div. 6-612.43-Ml 

12. Winding and Circuit Diagram of the 9"X9" Asymmetric 

Stark, Mark II Hydrophone, Leon W. Camp, M 01.- 
223-29, HUSL, June 10, 1943. Div. 6-612.71-M9 


CONFIDENTIAL 



466 


BIBLIOGRAPHY 


13. Harmonic Operation of Standard Projectors, Frederick V. 
Hunt, M 01.12-30, IIUSL, June 23, 1043. 

Div. 0-612.23-Ml 

14. Transducer Cable Shield with Conductimj Rubber, H. R. 
Stewart, M 113-52, HUSL, July 13, 1943. 

Div. 6-612.43-M2 

15. Transducer Diaphragms, Fred H. Smith, M 01.221-22, 

HUSL, July 14, 1943. Div. 6-612.8-M3 

16. Criticism of MOX and MKX Magnetostrictive Hydro¬ 

phones, Lyman N. Miller, M 61.036-372, HUSL, Aug. 
19, 1943. Div. 6-612.63-M3 

17. Sonar, Test and Analysis of Laminated Transducer Ele¬ 
ment, James W. Follin, Jr., Robert .\. Payne, Malcolm 
H. Hehb, M 02.45-87, HUSL, Sept. 17, 1943. 

Div. 6-612.71-M12 

18. Cycleweld, Francis P. Bundy, M 110.10-37, HUSL, Sept. 

18, 1943. Div. 6-612.44-M2 

19. The Nickel Laminated Stack, Leon W. Cam]), 

M 01.223-51, HUSL, Sept. 24, 1943. Div. 6-612.716-M3 

20. Visit to IFcst Lynn La6[aratory] of General Electric re¬ 
garding Materials for Permanent Magnets, Francis P. 
Bundy, M 113.50-59, HUSL, Sept. 25, 1943. 

Div. 6-612.42-M2 

21. General Ideas on Permanent Magnet Polarization of 

Magnetostrictive Transducers, Francis P. Bundy, M 01.- 
213-82, HUSL, Sept. 29, 1943. Div. 6-612.1-M3 

22. Magnetic Polarization of the Drisko T, Francis P. Bundy, 
M 01.213-84, HUSL, Se])!. 30, 1943. Div. 6-612.71-M13 

23. Tests on Some New DuPont Adhesives, G. W. Renner, 
M 113.50-62, HUSL, Oct. 4, 1943. Div. 6-612.44-M3 

24. Transducers, Thoughts on Laminated, Frederick V. Hunt, 
M 01.213-101, HUSL, Oct. 25, 1943. Div. 6-612.71-M15 

25. Transducers, Thoughts on Laminated, Eric A. Walker, 
M 01.213-102, HUSL, Oct. 25, 1943. Div. 6-612.71-M14 

26. Laminated Transducers, Further Thoughts on, kJ-ancis P. 
Bundy, M 01.213-104, HUSL, Nov. 2, 1943. 

Div. 6-612.71-M16 

27. Blister Rubber Paint, Francis P. Bundy, M 113.50-74, 

HUSL, Nov. 9, 1943. Div. 6-612.44-M5 

28. Sword Arm Transducer for Depth Determining Gear, 
Frederick V. Hunt, M 02.50-10, HL"SL, Dec. 4, 1943. 

Div. 6-612.717-Ml 

29. Design, Construction, and Performance of SPEP-1 Trans¬ 

ducer, Leon W. Camp, Francis P. Bundy, M 66.036-98, 
HUSL, Dec. 8, 1943. Div. 6-612.716-M4 

30. Sword Depth Finding Hydrophone, Robert B. Watson, 
M 02.50-13, HUSL, Dec. 18, 1943. Div. 6-612.717-M2 

31. A Study of the Behavior of Consolidated and Uncon¬ 

solidated Stack Transducers in Castor Oil and in Water, 
Leon W. Camp, Francis P. Bundy, M 01.213-134, 
HUSL, Jan. 13, 1944. Div. 6-612.71-M21 

32. Calibrations and Patterns of SPEP Model No. 1 [and] 
No. J [with] Four Quadrants in Parallel, Nelson K. 
Moody, Jr., M 66.016-146, HUSL, Jan. 24, 1944. 

Div. 6-612.716-M5 

33. A Study of PM Polarized SPEP Elements, Francis P. 
Bundy, M 66.036-148, HUSL, Jan. 26, 1944. 

Div. 6-612.716-M6 

34. Concluding Report on Bookphones, G. W. Renner, 
M 01.223-66, HUSL, Feb. 7, 1944. Div. 6-612.71-M22 


35. Effiriencies of Consolidated and Unconsolidated Stack 
Transducers in Castor Oil and in Water (External Memo¬ 
randum), Francis P. Bundy, Leon W. Camp, NDRC 
6.1-sr287-1356, HUSL, Feb. 10, 1944. 

Div. 6-612.71-M23 

36. Results of Drop Tests of SPEP-3, Nos. 1 and 3, Francis 

P. Bundy, Leon W. Camj), M 66.436-170, HUSL, Feb. 
12, 1944. Div. 6-612.716-M7 

37. Design, Construction, and Performance of the DT I'rans- 

ducer, Benjamin B. Drisko, M 01.223-78, HUSL, Feb. 
28, 1944. Div. 6-612.71-M24 

38. Shading for d" Xb'" SPEP T ransducer for General Electric, 

Nelson M. Blachman, M 66.036-l!)2, HUSL, Mar. 9, 
1944. Div. 6-612.716-M8 

39. Coupling Tests on Segmented and Unsegmented Ladder- 

phone Stacks, LDPI No. 1 and No. 3, William T. 
Bartholomew, F. P. Bundy, M 01.213-173, HUSL, Mar. 
16, 1944. Div. 6-612.31-xM8 

40. Rubber for Underwater Use, Alan H. Selker, M 113.50-10!), 

HUSL, Mar. 31, 1944. Div. 6-612.43-M3 

41. Coupling Tests on Ladder phone Stacks, Frederick V. 
Hunt, M 01.213-183, HUSL, Apr. 10, 1944. 

Div. 6-612.71-M26 

42. Instructions for Construction, Testing, and Assembly of 

G.E. SPEP Transducers, Francis P. Bundy, M 66.036- 
241, HUSL, Apr. 15, 1944. Div. 6-612.716-M9 

43. Instructions for Construction, Testing, and Assembly of 
Harvard SPEP Transducers, Fh'ancis P. Bundy, M 66.- 
036-247, HUSL, Apr. 19, 1944. Div. 6-612.716-MlO 

44. Handling Equipment for Cleaning, Annealing, and Coating 

Nickel Laminations, Paul E. Sabine, M 110.10-127, 
HUSL, Apr. 20, 1944. Div. 6-612.41-M18 

45. Suggested Tests of Acoustical Transparency and Damping 
of Rubber and Rubber Substitutes, Francis P. Bundy, 
M 01.21-70, HUSL, May 2, 1944. Div. 6-612.43-M4 

46. Stepped Frequency Transducers, G. W. Renner, Francis 
P. Bundy, M 01.223-90, HUSL, May 4, 1944. 

Div. 6-612.71-M27 

47. Acoustic Loading Tests on Transducers with Narrow 
Radiating Faces, Francis P. Bundy, Milton R. Carlson, 
M 01.21-71, HUSL, May 11, 1944. Div. 6-612.716-Mll 

48. Transmission and Reflection Characteristics of Rubber 
Discs, Natural and GR-S (Artificial), Jack C. Cotton, 
M 113.5-122, HUSL, May 11, 1944. Div. 6-612.43-M5 

49. Tran.sducers Separated from the Water by Rubber or Oil, 
Nelson M. Blachman, M 01.21-72, HUSL, May 12, 1944. 

Div. 6-612.43-M6 

50. Rubber-Covered SPEP Element, G. W. Renner, M 01.213- 

197, HUSL, May 15, 1944. Div. 6-612.43-M7 

51. Miracle Adhesives, Francis P. Bundy, Leon W. Camj), 
M 113.5-127, HUSL, May 18, 1944. Div. 6-612.44-MlO 

52. Transmission Loss in Natural and Synthetic Rubbers, 
Paul E. Sabine, M 113.5-130, HUSL, May 24, 1944. 

Div. 6-612.43-M8 

53. Transmission and Reflection Characteristics of Rubber 
Di.scs, Natural and Artificial [Part] II, Jack C. C^otton, 
M 113.5-134, HUSL, June 3, 1944. Div. 6-612.43-M9 

54. Transmission and Density Te.sts ou Twenty-One Natural 

Rubber Discs, Jack C. Cotton, M 113.5-136, HUSL, 
June 9, 1944. Div. 6-612.43-MlO 


CONFIDENTIAL 



BIBLIOGKArilY 


467 


55. SPEP Beam Palierns, R. C. McLoughlin, M 66.036-391, 

HUSL, .June 13, 1944. Div. 6-612.716-M12 

56. More Transmission Tests, Tyler No. 212, Rubberized 
Canvas, Neoprene [and] pc Rubber, Jack C. Cotton, 
M 113.5-138, IIUSL, June 14, 1944. Div. 6-612.43-Mll 

57. Lamination Design to Minimize the Q, Nelson M. Blacli- 
maii, M 01.213-200, HUSL, June 17, 1944. 

Div. 6-612.34-M6 

58. Design, Construction and Performance of the fJU kc Sword 
Arm Depth Angle Transducer, G. W. Renner, Francis P. 
Bundy, M 02.50-56, HUSL, July 1, 1944. 

Div. 6-612.717-M3 

59. SPEP Faces, Francis P. Bundy, IVI 66.036-449, HUSL, 

July 10, 1944. Div. 6-612.716-M13 

60. Transmission Tests, 15 Tyler Rubber No. 212 SPEP 

Faces, July S, 19U, -Lick C. Cotton, M 01.213-209, 
HUSL, July 10, 1944. Div. 6-612.43-M12 

61. The Construction and Performance of the Whale Trans¬ 
ducer (Preliminary Report), Milton R. CarLson, Franci.s 
P. Bundy, M 91.236-129, HUSL, July 16, 1944. 

Div. 6-612.71-M29 

62. Consolidation of Nickel Laminations, Leon W. Camp, 
M 02.453.2-49, HUSL, July 26, 1944. Div. 6-612.44-Mll 

63. Density and Transmission Tests on Nineteen SPEP 

Discs, Jack C. Cotton, M 66.036-486, HUSL, July 28, 
1944. Div. 6-612.716-M14 

64. Preliminary Results on High Level Pulsing of a Single 

SPEP Element, Roger W. Hickman, M 01.213-239, 
HUSL, Sept. 25, 1944. Div. 6-612.716-M15 

65. Tests on a Production Unit of SPEP Transducer Made by 
the Gamewell Company, Jack C. Cotton, Paul FI. Sabine, 
M 01.213-242, HUSL, Sept. 28, 1944. 

Div. 6-612.716-M16 

66. Sound Transmission Loss of SPEP Face Made by Alfred 

Hale, Rubber Company, Paul FI. Sabine, M 66.036-581, 
HUSL, Oct. 4, 1944. Div. 6-612.43-M13 

67. Tests on Gamewell Production SPEP Units No. 3 and 

No. 4, Paul E. Sabine, Jack C. Cotton, M 01.213-249, 
HUSL, Oct. 10, 1944. Div. 6-612.716-M17 

68. Shading for Additional Minor Lobe Reduction in GE 

SPEP, Nelson M. Blachman, M 01.213-266, HUSIy, 
Oct. 25, 1944. Div. 6-612.716-M18 

69. Tests and Analysis of British Scanning Sonar Transducer 

Element, F^rancis P. Bundy, M 02.45.7-120, Hl’SL, 
Oct. 25, 1944. Div. 6-612.55-M16 


70. Measurement on SPEP Stacks Cemented to Various 
Diaphragms, Rubber, Stainless Steel, [and] Plastic, Jack 
C. Cottcm, M 66.036-676, HUSL, Nov. 24, 1944. 

Div. 6-612.43-M14 

71. Some Observations on the Effect of Current Amplitude and 

Temperature on the Characteristics of a Single SPEP 
Element (MINI-SPEP), Roger W. Hickman, M 01.213- 
287, HUSL, Nov. 29, 1944. Div. 6-612.716-M 19 

72. Lamination Cleaning, Jack C. Cotton, M 110.1-158, 

HUSL, Dec. 1, 1944. Div. 6-612.71-M31 

73. Variation of Magnetization in Legs of PM Polarized 

SPEP Element with Driving Field, S. T. Pan, M 01.213- 
291, HUSL, Dec. 6, 1944. Div. 6-612.41-M21 

74. Reversible Permeability and Hysteresis Loss in Oxide- 
Annealed [Grade] A Nickel Polarized at B» = 4100, 
S. T. Pan, M 113.5-180, HUSL, Dec. 12, 1944. 

Div. 6-612.41-M22 

75. Test Results on SPEP’s 6-22, -23, -24 {Gamewell-5, -6, -7), 
Jack C. Cotton, M 66.016-741, HLISL, Jan. 15, 1945. 

Div. 6-612.716-M20 

76. Rubber Faces for Leeds and Norlhrup SPEP Transducers, 
F’rancis P. Bundy, M 66.636-774, HLISL, Feb. 23, 1945. 

Div. 6-612.43-M15 

77. Tests Results on T wo GE Type SPEP Units Made by 
Leeds and Northrup, Francis P. Bundy, Jack C. Cotton, 
M 66.016-784, HUSL, Mar. 15, 1945. 

Div. 6-612.716-M21 

78. Test Results on SPEP’s 6-25, -26, -27 {Gamewell-8, -!), 

-10), Jack C. Cotton, M 66.016-816, HUSL, Apr. 9, 
1945. Div. 6-612.716-M22 

79. Sound .\ttenuation in Coating Materials, Alan H. Selker, 

G. W. Renner, M 01.21-128, HUSL, Apr. 9, 1945. 

Div. 6-612.43-M16 

80. Organic Cements in Underwater Sound Apparatus, .Alan 

H. Selker, M 113.5-185, HUSL, .Apr. 18, 1945. 

Div. 6-612.44-M14 

81. Some Applications of Organic Pla.stics and Rubber in 

Underwater Sound Apparatus, .Alan H. Selker, M 113.5- 
191, HUSL, May 26, 1945. Div. 6-612.43-M17 

82. MOX and MKX Magnetostriction Hydrophones [R. h. 

Peek], Case 23240, Report 2210-RLP-MS, BTL, .June 
10, 1943. Div. 6-612.63-M2 

83. Task No. .{B, Modification of QC-Type Projector (F'inal 
Report), Section 6.67, 1^. S. Navy BuShips, Sonar De¬ 
velopment Contract NX .sr-46932 with Western FJectric 
Co., Inc., BTL, Dec. 1, 1944. 


(Chapter 8 


1. Laminated Magnetostriction Tubes, Malcolm H. Hebb, 
M 01.213-07.1, HUSL, Nov. 7, 1942. Div. 6-612.63-Ml 

2. The Construction of the “Tomato-Can” MS Tube Tester 

and the Results Obtained with It, Francis P. Bundy, M 
01.10-20, HUSL, Nov. 11, 1942. Div. 6-612.8 M1 

3. Efficiency and Sensitivity of Cone-Type Magnetostriction 

Transducers, Harvey A. Brooks, M 01.213-18, HUSL, 
Jan. 4, 1943. Div. 6-612.22-M8 


4. Angular Characteristics of the WEA-1 Used as a Hydro¬ 
phone (Memorandum for File), FJdward Gerjuoy, Re¬ 
port G13/176, CUDWR-NLL, Mar. 2, 1943. 

Div. 6-556.1-M9 

5. Liquid within Dome, Addition of Aerosol, H. W. Hender¬ 
son, M 01.12-21, HUSL, Apr. 22, 1943. 

Div. 6-612.44-Ml 

6. Spherical WEA-1 Projector, FVancis P. Bundy, M 02-21, 

HLTSL, June 17, 1943. Div. 6-612.8-M2 


CONFIDENTIAL 



468 


BIBLIOGRAPHY 


7. Heduction of Eddy Currents in Magnetostrictive Tubes, 
Malcolm H. llehb, M 01.213-62, HUSL, July 24, 1943. 

Div. 6-612.8-M4 

8. Line Source Transducer and Possible Sonar Application, 
Roland E. Mueser, M 02.45-70, HUSL, July 30, 1943. 

Div. 6-612.62-M12 

9. Spherical WEA-1 Projector for Aide de Camp, F'rancis P. 
Bundy, M 02-23, Hl'SL, Aug. 14, 1943. 

Div. 6-612.8-M5 

10. Optimum Coil Location for MS Transducers, Frederick 
V. Hunt, M 01.213-77, HUSL, Sept. 2, 1943. 

Div. 6-612.8-M6 

11. Preliminary Impedance Measurements Which Led to the 
Design of the Honeycomb {19 Element) Transducer, P. M. 
Kendig, M 60.0360-254, HUSL, Sept. 20, 1943. 

Div. 6-612.7-Ml 

12. Results of Spy Pond Tests on Waffle Iron EP Transducer, 

Nelson K. Moody, Jr., M 66.236-23, HUSL, Sept. 21, 
1943. Div. 6-612.55-M4 

13. Further Studies of Optimum Coil Location for Nickel Tube 

Transducers, Nelson K. Moody, Jr., M 01.213-80, HUSL, 
Sept. 27, 1943. Div. 6-612.8-M7 

14. The 4-Tube Hydrophone, H. K. Stewart, M 60.0360-301, 

HUSL, Oct. 1, 1943. Div. 6-612.8-M8 

15. Performance Variations in Tube Type MS Transducers, 

Benjamin B. Drisko, M 60.0360-323, HUSL, Oct. 6, 
1943. Div. 6-612.8-M9 

16. Titbe Driven Transducer Design Considerations, Francis 

P. Bundy, Harold P. Knauss, John D. Lane, M 02.45.- 
20-43, HUSI,, Dec. 8, 1943. Div. 6-612.8-Mll 


17. Measurements on Galaxy QC Head and Associated Wiring, 

J. F. Hersh, James J. Faran, Jr., M 02.07-46, Hl’SL, 
Apr. 24, 1944. Div. 6-612.8-M14 

18. Patterns of 12-Tube Hydrophones, Lyman N. Miller, 
M 60.036-1074, HUSL, Jan. 15, 1945. 

Div. 6-612.8-M19 

19. Twelve-Tube Hydrophone, R. \V. Marsh, M 60.036-1094, 

HUSL, Jan. 24, 1945. Div. 6-612.8-M20 

20. Calibration of Experimental QCU Projectors, Models No. 

1 and No. 2, Eginhard Dietze, NDRC 6.1-srl 130-2138, 
USRL, Feb. 24, 1945. Div. 6-556.1-M34 

21. Some Applications of Organic Plastics and Rubber in 

Underwater Sound Apparatus, .Wan ll. Selker, M 113.5- 
191, HUSL, May 26, 1945. Div. 6-612.43-M17 

22. Analysis of QC and JK Type Projectors [Summary of 

(1) Report 2420-WDG-ED-VP, Mar. 18, 1942; (2)'Re- 
port 2420-WDG-ED-Hl, Mar. 18, 1942; and (3) Report 
2420-WDG-ED-MA, Mar. 27, 1942], Walter D. 

Goodale, Jr., Eginhard Dietze, NDRC C4-sr212-077, 
BTL, Apr. 10, 1942. (1) Div. 6-554-MlO 

(2) Div. 6-556.1-Ml 

(3) Div. 6-554.1-Ml 

23. Measuring Tank Suitable for Acoustic Measurements in 

Water, R. L. Jones, 6.1-NDRC-836, BTL, Mar. 31, 
1943. Div. 6-553.4-M2 

24. Task No. jB, Modification of QC-Type Projector (Final 
Report), Section 6.67, U. S. Navy BuShips, Sonar De¬ 
velopment Contract NX sr-46932. Western Electric Co., 
Inc., BTL, Dec. 1, 1944. 

25. U. S. Patent 2,063,951, R. I.. Steinberger, Dec. 15, 1936. 


Chapter 9 


1. Underwater Impedance Measurements, R. L. Brown, John 
R. Pellam, NDRC C4-sr287-093, HUSL, May 8, 1942. 

Div. 6-612.511-Ml 

2. Underwater Impedance Measurements (Condensed Re¬ 
port), Richard L. Brown, John R. Pellam, NDRC 
C4-.sr287-094, HUSL, May 8, 1942. Div. 6-612.511-M2 

3. Comments on Underwater Impedance Measurements, 
R. L. Brown, John R. Pellam, H. T. O’Neill, NDRC 
C4-sr287-094, [Report] 264.1, UCDWR, Aug. 12, 1942. 

Div. 6-612.511-M3 

4. Capacity of Ground in Calibration of Transducers, Harvey 

.A. Brooks, Malcolm H. Hebb, M 01.10-27, HUSL, 
Feb. 1, 1943. Div. 6-612.51-M2 

5. Bell Laboratories’ Ab.sorbent-Lined Tank, K. N. Fromm, 
Paul E. Sabine, M 01.11-18, HUSL, Mar. 9, 1943. 

Div. 6-612..53-.M2 

6. Direct Measurement of Complex Impedance, O. Hugo 
Schuck, M 01.10-32, HUSL, Mar. 31, 1943. 

Div. C-612.511-M4 

7. Comparison f Data Taken at Barge and Fur-Lined Bath¬ 

tub, R(d>ert B. Watson, M 01.10-40, HI SL, June 14, 
1943. Div. 6-612..53-M5 

8. Fourth Floor Impedance Measurements, P. M. Kendig, 
M 60.21-174, HUSL, Aug. 23, 1943. Div. 6-612.511-M5 


9. Amplifier and Power Supply for Harvard Laboratory, 
F. P. Herrnfeld, Sylvester .1. Haefner, Report 630 569, 
NL 165, CUDWR-NLL, Oct. 25, 1943. 

Div. 6-612.53-M6 

10. Sound Apparatus Recorders, J. F. Hersh, M 110.50-83, 

HUSL, Dec. 10, 1943. Div. 6-612.53-M7 

11. The Geometrical Inversion Transformation and Its Ap¬ 

plication in the Admittance-Impedance Relations, An¬ 
alytical Admittance-Impedance Relations, Robert E. 
Payne, Malcolm H. Hebb, M 01.213-141, HUSL, Jan. 
26,1944. Div. 6-612.32-Ml 

12. New London Measuring Amplifier, H. Newburg, M 110- 

250, HUSL, Feb. 2, 1944. Div. 6-612.53-M9 

13. New London Measuring Amplifier, Fred H. Smith, 
M 110-251, HUSL, Feb. 3, 1944. Div. 6-612.53-MlO 

14. .4 Power Amplifier and Bridge for the Measurement of 

Impedance at High Power Level (Memorandum for File), 
Sylvester J. Haefner, Report P35 653, CUDWR-NLL, 
Feb. 15, 1944. Div. 6-612..53-M11 

15. Effect of Cable on tho Measure I Voltage Terminal of a 
Transd icer, Lou Fein, M 01.21-53, HU.sL, Feb. 22, 1944. 

Div. 6-612.51-M7 

16. Development of Bridge Circuits for the Measurement of the 

Transducer Characteristics, Robert E. Payne, M 01.10- 
120, HUSL, .Apr. 21, 1944. Div.'6-612.53-M12 


C'(3XFIDENTIAL 



BIBLIOGRVPHY 


469 


17. Transducers Separated from the Water by Rubber or Oil, 
Nelson M. Hlachinan, HUSL, May 12, 1944. 

Div. 6-612.43-M6 

18. Measurement of Reflection Coefficient, M. H. Hehb, Nelson 
M. Blachman, M 01.21-74, HUSL, May 19, 1944. 

Div. 6-612.51-M9 

19. Production Testing of Projectors, Erwin F. Schroder, 

NDRC 6.1-srl 130-1622, NS-182, USRL, May 22, 
1944, p. 9. Div. 6-o52-Mll 

20. Fairprene for Absorbent Tank Linings, /?e/[erence] Dr. 
Hunt’s 4/ewio[randum3 of July 1944, Paul E. Sabine, 
M 113.5-154, HUSL, July 26, 1944. Div. 6-612.53-M15 

21. The Varistor Conductometer, .1. F. Hersh, James J. 
Faran, Jr., M 01.10-143, HUSL, Sept. 20, 1944. 

Div. 6-612..53-M16 

22. Artificial Transducers for Scanning Sonar, Robert K. 
Payne, M 91.20-242, HUSL, Oct. 30, 1944. 

Div. 6-612.53-M17 

23. The Conductometer, James J. Faran, Jr., M 01.10-164, 

HUSL, Nov. 17, 1944. Div. 6-612..53-M18 

24. Networks with 90 Degrees Difference in Phase over Two 

Octaves, C. W. Horton, M 110.3-165, HUSL, Dec. 11, 
1944. Div. 6-612.3-M3 

25. The Vector Impedance Locus Plotter, J. F. Hersh, James 
J. Faran, Jr., M 01.10-170, HUSL, Mar. 2, 1945. 

Div. 6-612..53-M20 

26. Design of Potentiometer Phase Shifter for Phase Measure¬ 
ments over a Broad Frequency Rand, Robert L. Cum- 
merow, M 110-373, HUSL, Mar. 5, 1945. 

Div. 6-612.53-M21 

27. Vector Impedance Locus Plotter, J. F. Hersh, James J. 

Faran, Jr., M 01.10-170, NDRC 6.1-sr287-2175, HUSL, 
Mar. 15, 1945. Div. 6-612.53-M22 

28. Transducer Research and Production at the New London 
Laboratory, William B. Snow, James W. Follin, Jr., 
Wilbur T. Harris, NDRC 6.1-srl 128-2212, Report G12/- 
1418, NS-113, CUDWR NLL, May 25, 1945. 

Div. 6-612.1-M8 

29. Mechanical and Acoustic Attachments for Piezoelectric 
Crystals Csed in I'ransducers, NDRC 6.1-sr346-628, 
Div. 6, Vol. 12, BTL, Dec. 15, 1942. 

30. Acoustic Tank, Arthur C. Keller, Case 37866-1, Report 
2210-ACK-MS, BT-63, BTL, Mar. 8, 1943. 

Div. 6-553.4-M1 

31. Measuring Tank Suitable for Acoustic Measurements in 
lUaler. 6.1-NDRC-836, BTL, Mar. 31, 1943. 

Div. 6-.5.53.4-M2 


32. “High Frequency Resistance Standard,” W. D. Voelker, 
Bell Laboratories Record, Vol. NIII, No. 5, January 1935. 

33. “.V .5-Megacycle Impedance Bridge,” C. H. Young, Bell 
Laboratories Record, Vol. XV, No. 8, .Ypril 1937. 

34. “.\n Electronic Null Detector for Impedance Bridges,” 
Horatio W. Lamson, The Review of Scientific Instruments, 
Vol. 9, 1938, pp. 272-275. 

35. “.\ New Type of Selective Circuit and .\pplications,” 
H. H. Scott, Proceedings of the Institute of Radio En¬ 
gineers, Vol. 26, No. 2, February 1938. 

36. “.\n Inductance and Capacitance Bridge,” S. J. Zam- 
mataro. Bell Laboratories Record, Vol. XVI, No. 10, 
June 1938. 

37. “The 17B Oscillator,” W. J. Means, Bell Laboratories 
Record, Vol. XVII, No. 9, May 1939. 

38. “.Applications of Copper Oxide Rectifiers,” Leo L. 
Beranek, Electronics, Vol. 12, July 1939, p. 15. 

39. “.Applications of Negative Feedback with Particular 
Reference to Laboratory Equipment,” F. E. Terman, 
R. R. Bu.ss, W. R. Hewitt, F. C. Cahill, Proceedings of 
the Institute of Radio Engineers, A’ol. 10, October 1939, 
p. 649. 

40. “Bridged-T and Parallel-T Null Circuits for Measure¬ 
ments at Radio Frequencies,” W. N. Tuttle, Proceedings 
of the Institute of Radio Engineers, Vol. 28, 1940, pp. 
23-29. 

41. “.A Bridge for Mea.suring Core Lo.s.s,” H. T. Wilhelm, 
Bell Laboratories Record, A’ol. XIX, No. 3, November 
1940, p. 94. 

42. “Some Characteristics of a Stable Negative Resistance,” 
Cledo Brunetti, Leighton Greenough, Proceedings of the 
Institute of Radio Engineers, Vol. 13, December 1942, 
pp. 542-546. 

43. Alternating Current Bridge Methods, B. Hague, Sir Isaac 
Pitman and Sons, Ltd., London, Eng., 1943, pp. 566-571. 

44. Radio Engineers’ Handbook, f'. E. Terman, McGraw- 
Hill Book Co., New A'ork, N. Y., 1943, p. 943. 

45. “High Selectivity at .Audio and Intermediate Fre¬ 
quencies,” E. Lloyd Thomas, lUfre/m World, Vol. 50, 
No. 6, June 1944, pp. 175-178. 

46. “Electronics in the Study of Head Injuries,” Charles 
Sheer, John G. Lynn, Electronics, Vol. 17, .lanuary 1944, 
p. 114. 

47. “.A Cathode-Ray Bridge Detector,” E. H. Eveland, Bell 
Laboratories Record, Vol. XXIII, No. 3, March 1945. 

48. “Impedance Bridge with a Billion-to-One Range,” H. T. 
Wilhelm, Bell Laboratories Record, Vol. XXIII, No. 3, 
March 1945. 


Chapter 10 


1. Intercomparison of Microphones between MIT Project 
Die 5985 and Other Groups, [Report from] January 1, 
1941 to February , 14 , l'^4L C’UDWR-NLL, Fel). 24, 1942. 

Div. 6-612.55-Ml 

2. Listening Tests on Thuras Doughnut Hydrophone, D. P. 
Loye, Report G12 2679, CUDWR-NLL, Apr. 30, 1942. 

Div. 6-612.62-Ml 


3. Noise Level in Small Magnetostriction Hydrophones, 

William B. Snow, Rejiort D16 '2814, CUDWR-NLL. 
May 15, 1942. Div. 6-612.22-M4 

4. Mechanical Driver for Testing d'X'J" Maynetostrietton 

Hydrophone, W. L. Widlar, Report D16.2 '3716, 
CUDWR-NLL, Aug. 17, 1942. Div. 6-612.53-Ml 


COXFIDEXTIAI 



470 


BIHLKMiKArUY 


5. Free Field Reciprocity Calibration of Underwater Sound 
Laboratories’ Standards, Leslie L. Foldy, NDRC 
C4-sr20-206, USRL, Sept. 11, 1942. Div. 6-5.52-M3 

6. The Relation Between the Absolute Efficiency of a Hydro¬ 
phone and Its Thermal Noise Level, Eginhard Dietze, 
NDRC C4-sr20-.593, Dec. 11, 1942. Div. 6-5.52-M5 

7. Capacity of Ground in Calibration of Transducers, Harvey 

A. Brooks, Malcolm H. Hehh, M 01.10-27, HUSL, Feb. 
1, 1943. Div. 6-612.51-M2 

8. Status of Barge Plans, Robert L. Cummerovv, M 01.10-31, 

HUSL, Mar. 10, 1943. Div. 6-612.52-Ml 

9. Markers for Frequency Scale in Measurement Set-Up, 
O. Hugo Schuck, M 01.10-37, HUSL, Apr. 5, 1943. 

Div. 6-612..53-M3 

10. Characteristics of GB5-2 and C-26 Transducers, Fklward 

Gerjuoy, Report G12/298, CUDWR-NLL, Apr. 22, 
1943. Div. 6-612.55-M2 

11. Results of Reciprocity Calibration as Applied to Hebb- 

phone No. 4, Robert L. Cummerow, M 01.213-40, 
HUSL, May 12, 1943. Div. 6-612.512-M2 

12. Comparison of Data Taken at Barge and Fur-Lined Bath¬ 

tub, Robert B. Watson, M 01.10-40, HUSL, June 14, 
1943. Div. 6-612.53-M5 

13. Temperature Dependence of Our 6"x6’' X-Cut Crystal 
Projector, Precision of Barge Measurements, Paul FI. 
Sabine, M 01.212-10, HUSL, .June 22, 1943. 

Div. 6-612.54-M3 

14. Direction of Rotation of Transducers in the Measurement 

of Directivity Patterns, Robert L. Cummerow, M 01.1045, 
HUSL, July 3, 1943. Div. 6-612.51-M3 

15. Spy Pond Equipment, Paul Ebaugh, M 110.20-25, 

HUSL, July 8, 1943. Div. 6-012..52-M2 

IG. Sign Convention in Pattern Measurements, Frederick V. 

Hunt, M 01.10-53, HUSL, July 14, 1943. 

Div. 6-612.21-M5 

17. “3A Standard Cry.stal Hydrophone,” Oct. 1, 1942, Card 
No. 50 Practical Dictionary of Underwater Acoustical 
Devices, and Supplementary Loose Leaf Sheets, NDRC 
6.1-.sr20-889, OSRD 772, USRL, July 27, 1943. 

Div. 6-554-M28 

18. “Asidic Echo Ranging Receiver,” Card No. 55 Practical 
Dictionary of Underwater Acoustical Devices, and Sup¬ 
plementary Loose Leaf Sheets, NDRC 6.1-sr20-889, 
OSRD 772, USRL, July 27, 1943. Div. 6-554-M28 

19. “IK Type Projector (superceding I.J Type),” Card No. 
57 Practical Dictionary of Underwater Acoustical Devices, 
and Supplementary Loose Leaf Sheets, Vol. 1, OSRD 772, 
NDRC 6.1-sr20-889, I'SRL, July 27, 1943. 

Div. 6-554-M28 

20. “HIv Series Crystal Hydrophones,” Jan. 19, 1944, Card 
No. 84 Practical Dictionary of Underwater Acoustical 
Devices, and Supplementary Loose Leaf Sheets, Vol. 1. 
OSRD 772, NDRC 6.1-sr20-889, USRL, July 27, 1943- 

Div. 6-554-M28 

21. “5E Crystal Hydrophone,” Mar. 20, 1944, Card No. 126 
Practical Dictionary of Underwater Acoustical Devices, 
and Supplementary Loose Leaf Sheets, OSRD 772, 
NDRC 6.1-sr20-889, USRL, July 27, 1943. 

Div. 6-.554-M28 


22. ‘‘2.\ Pressure Gradient Hydrophone,” Oct. 5, 1944, Card 
No. 128, Practical Dictionary of Underwater Acoustical 
Devices, and Supplementary Loose Leaf Sheets, OSRD 
772, NDRC G.l-sr20-889, USRL, July 27, 1943. 

Div. 6-554-M28 

23. “NPA Crystal Projector,” Oct. 5, 1944, Card No. 133, 
Practical Dictionary of Underwater Acoustical Devices, 
and Supplementary Loose Leaf Sheets, Vh)l. 1, OSRD 772, 
NDRC G.l-sr20-889, USRL, July 27, 1943. 

Div. 6-5.54-M28 

24. Absorbent Lined Tank for SGM Monitor Tests, Paul E. 
Sabine, M 02.331.37-lG, HUSL, Aug. IG, 1943. 

Div. G-612.52-M3 

25. First Reciprocity Measurements at Spy Pond, Robert E. 
Mueser, M 01.10-7G (1), HUSL, Sept. 21, 1943. 

Div. 6-G12.512-M3 

26. Sensitivity of Standard Hydrophones, Paul E. Sal)ine, 
M 01.10-79, HUSL, Sept. 23, 1943. Div. 6-612.54-M4 

27. Projector Test Gear for Field Testing of Echo Ranging 
Projectors, NDRC 6.1-sr287-lIGO, HUSL, Oct. 15, 1943. 

28. The 4th and 5th Reciprocities at Spy Pond and Summary, 

Robert Fh Mue.ser, M 01.10-7() (4-5), HUSL, Nov. 15, 
1943. Div. 6-612.512-M4 

29. Directivity Index Data Sheets, .lack C. Cotton, M 01.- 

10-90, HUSL, Dec. 10, 1943. Div. G-612.51-M4 

30. Sound Apparatus Recorders, J. F\ Hersh, M 110.60-83, 

HUSL, Dec. 10, 1943. Div. 6-612.53-M7 

31. Directional Pattern Tracer, Robert B. Watson, M 02.- 

333-23, HUSL, Jan. 19, 1944. Div. 6-612.53-M8 

32. Field and Pattern of 3y.l2 X-Cut Crystal Transducer 

Made by M. I. T., Paul E. Sabine, M 01.212-50, HUSL, 
Jan. 20, 1944. Div. 6, Vol. 12 

33. A Power Amplifier and Bridge for the Measurement of 

Impedance at High Power Level (Memorandum for File), 
Sylvester J. Haefner, Report P35 653, CUDWR-NLL, 
F'eb. 15, 1944. Div. G-612..53-M11 

34. Broad Frequency Reciprocity Calibration of Standards, 
Robert E. Mueser, M 01.213-154, HUSL, F’eb. 16, 1944. 

Div. 6-612.512-M6 

35. Simplified Conversion Procedure for Field and Frequency- 

Response Data, Jack C. Cotton, M 01.10-97, HUSI^, 
Feb. 18, 1944. Div. 6-612.51-M6 

36. Field and Frequency Response Sheet for B-19B No. 18 
Standard, Simplified Conversion Procedure, Jack C. 
Cotton, M 01.213-165, FIUSL, F>b. 29, 1944. 

Div. 6-612.611-M12 

37. New Thermal Wattmeter, Mountain Lakes Design, Jack 
C. Cotton, M 01.10-124, HUSL, May 3, 1944. 

Div. 6-612..53-M13 

38. Secondary Tuning Fork Frequency Standard and Har¬ 

monic Generator, Paul Ebaugh, M 01.10-127, HUSL, 
May 15, 1944. Div. 6-612..53-M14 

39. Sweetwater Lake Calibration Station, N. J. Holter, FIUSL 
File N52. FTCDWR, July 20, 1944. 

40. Fairprene for Absorbent Tank Linings, J^e/Cerence] Dr. 
Hunt’s Mewo[randum] of July 24', 1944, Pnul E. Sabine, 
M 113.5-1.54, HUSL, July 26, 1944. Div. 6-612.53-M15 

41. Recent Measurements on Standard Hydrophone B-19B 
No. 18, B-19H No. 2, and B-19B No. 1, Paul Ebaugh, 
M 01.213-215, HUSL, Aug. 4, 1944. 

Div. 6-612.611-M19 


CONFIDENTIAL 



RIHLIOGKAPHY 


471 


42. Overload Pressure on a B-lOH Type Transdueer, Lou 
Fein, B. Powers, M 01.213-216, HUSL, .\ug. 4, 1944. 

Div. 6-612.613-M8 

43. Field Variations at the Barge, Lou Fein, .\. B. Powers, 
M 01.10-140, HUSL, Aug. 7, 1944. 

Div. 6-612.51-MlO 

44. Characteristics of B-19H Hydrophone Used as Projector, 

Paul E. Sat)ine, Paul Ehaugh, M 02.331.7-85, HUSL, 
.\ug. 7, 1944. Div. 6-612.613-M9 

45. Calibration of HUSL HP-j Laminated Stack Transducer, 

Sword and Depth Angle Transducer, and B-19H Hydro¬ 
phone, Eginhard Dietze, XDKC 6.1-srl 130-1826, 
USRL, Aug. 28, 1944. Div. 6-556.1-M27 

46. Hydrophone Tests Adopted at the New London Laboratory 
of Columbia University, Division of W ar Research, William 
B. Snow, XDKC 6.1-srl 121-1849, Report G12 1092, 
CUDWR-NLL, Sept. 1, 1944. Div. 6-612.51-Mll 

47. Sensitivities of B-19B No. 6 and B-19H No. 1 Standard 
Hydrophones Used at the Barge, Lou Fein, A. B. Powers, 
M 01.213-232, HUSL, Sept. 20, 1044. 

Div. 6-612.611-M20 

48. Sensitivity of B-19K No. 1 Standard Hydrophone Used 

at the Barge, Lou Fein, L. C. Foster, M 01.213-2.54, 
HUSL, Oct. 17, 1944. Div. 6-612.615-Ml 

49. Measurements of High Impedance Transducers at the 

Barge, Even If One Side Is Grounded, Lou Fein, M 01.10- 
160, HUSL, Xov. 15, 1944. Div. 6-612.511-M7 

50. Portable Polar Chart Recorder (Status Report), X'S-142, 

HUSL, Dec. 1, 1944. Div. 6-612.53-M19 

51. Sensitivity of B-19K No. 1, Lou Fein, M 01.213-293, 

HUSL, Dec. 8, 1944. Div. 6-612.615-M2 

52. Suggested Simplifications in Testing at Spy Pond, Robert 
E. Mueser, M 60.016-1085, HUSL, ,Jan. 21, 1945. 

Div. 6-612.,52-M4 

53. Tests Adopted by the Hydrophone Standards Committee, 
July 10, 1944, William B. Snow, .James W. Follin, Jr., 
G. O. Rockwell, C. R. Sawyer, David W. Van Lerinep, 
T. E. Shea, Report G12/1342, NS-102 and NS-139, 
CUDWR-XLL, Jan. 27, 1945. Div. 6-612.51-M12 

54. Suggestions for Layout and Handling Gear at the Penn 

State Measurement Station, Paul Ebaugh, M 60.063-1119 
HUSL, Feb. 7, 1945. Div. 6-612.o2-M.5 

55. Sensitivities of B-19B No. 6 QP2, Lou PVin, Nelson M, 
Blachman, M 01.213-304, HL’^SL, Feb. 7, 1945. 

Div. 6-612.611-M22. 

56. Comments on Suggestions for Layout and Handling Gear 
at the Penn State Measurement Station, Francis P. Bundy, 
M 60.063-1147, HUSL, Feb. 20, 1945. 

Div. 6-612.52-M6 

57. Field Variations at the Sweetwater Lake Calibration Sta¬ 
tion of the University of California, Division of IFar Re¬ 
search, Paul Ebaugh, M 01.10-167, HLhSL, Feb. 20, 1945. 

Div. 6-612.51-M1.3 

58. The Nature of Field Intensity Variations at Spy Pond, 
Robert E. Mueser, M 01.10-168, HUSL, Feb. 21, 1945. 

Div. 6-612.51-M14 

59. Suggestions on Penn State Measurement Station, Rotrert 
E. Mueser, M 60.063-1186, HUSL, Mar. 14, 1945. 

Div. 6-612.52-M7 


60. Polar Pattern Plotting at Penn State, Harvey .\. Brooks, 
M 60.016-1203, HUSL, Mar. 23, 1945. 

Div. 6-612.53-M23 

61. Magnetostriction Dual-Purpose Projectors for Moshannon 

Test Station, Robert E. Mueser, J. R. Reitz, M 01.10-179, 
HUSL, Apr. 18, 1945. Div. 6-612.54-M5 

62. Reply to Memo[randum] April IS, 1945 [from] Robert E. 
Mueser and J. R. Reitz, Magnetostriction Dual Purpose 
Projectors for Black Moshannon Test Station, Paul 
Ebaugh, M 01.10-182, HUSL, .\pr. 24, 1945. 

Div. 6-612.54-MO 

63. Black Moshannon, N. Butz, Jr., M 60.063-1331, 

HUSL, May 19, 1945. Div. 6-612.52-M8 

64. Transducer Research and Production at the New London 
Laboratory, William B. Snow, James W. h’ollin, Jr., 
Wilbur T. Harris, XDRC 6.1-srll28-2212, Report 
G12/1418, CUDWR-NLL, May 25, 1945. 

Div. 6-612.1-M8 

65. How Not to Explain Field Variations, Lou Fein, Paul 

Ebaugh, Robert E. Mueser, M 01.10-198, HUSL, May 
28, 1945. Div. 6-612.51-M15 

66. Bubble Trouble Continued, Robert E. Mueser, M 01.10- 

200, HUSL, May 29, 1945. Div. 6-612.51-M16 

67. The Accuracy of an Acoustic Measurement [Memo¬ 

randum] A, Robert E. Mueser, M 01.1-203, HL’SL, 
June 6, 1945. Div. 6-612.51-M 18 

68. Spy Pond Standards, [Memorandum] B, Robert E. 
Mueser, M 01.1-204, HL"SL, June 6, 1945. 

Div. 6-612.52-M9 

69. A Calibrated Field for Hydrophone Testing [Memo¬ 

randum] C, Robert E. Mueser, M 01.1-205, HUSL, 
June 6, 1945. Div. 6-612.51-M17 

70. Field of QP No. 2 in May and June 1945, J. R. Reitz, 
M 01.213-334, HUSL, June 7, 1945. Div. 6-612.55-M17 

71. Electronic Layout for Black Moshannon, Paul Ebaugh, 
M 60.063.1391, HUSL, June 21, 1945. Div. 6-612.52-MlO 

72. Wetting Agents, Paul Ebaugh, M 01.10-207, HUSL, 

June 29, 1945. Div. 6-612.53-M24 

73. Portable Polar Chart Recorder and Servomechanism (Com- 

])letion Report), XDRG 6.1-sr287-2069, HUSL, Sept. 
15, 1945. Div. 6-553.5-M2 

74. Sound Gear Monitor, Underwater Sound Portable Test 
Equipment (Completion Report), XDRC 6.1-sr287-2086, 
HUSL, Xov. 1, 1945, pp. 106-107. Div. 6-641.1-M9 

75. A Primary Standard Pressure Gradient Hydrophone, 
XDRC C4-.sr212-058, BTL, Mar. 2, 1942. 

Div. 6-553.1-Ml 

76. A Subaqueous Projector for Hydrophone Calibration in the 
Audible Frequency Range, Reginald L. Jones, XDRC 
C4-sr212-103, BTL, June 1, 1942. Div. 6-553.2-M3 

77. A Standard Crystal Hydrophone, XDRC C4-sr212-507, 

BTL, Oct. 1, 1942. Div. 6-553.1-M2 

78. Operating Instructions for 2-4 and 3A Projectors, BTIj, 

Dec. 7, 1942. Div. 6-612.54-M2 

79. Standard Pressure Gradient Hydrophone (Operating 

Notes), Eginhard Dietze, Reports D-173204 and 
D-173206, BTL, May 3, 1943. Div. 6-612.53-M4 

80. irfdc Range Hydrophones for Low Sound Fields, OSRD 
Report, XDRC 6.1-sr346-1321, BTL, Mar. 20, 1944. 

Div. 6-553.1-M 7 


CONFIDENTIAL 



472 


BIBLIOGRAPHY 


Chapter 11 


1. Transducer Cable Shield with Conducting Rubber, II. K. 
Stewart, M 113-52, HUSL, .Ivily 13, 1943. 

Div. 6-612.43-IM2 

2. A Power Amplifier and Bridge for the Measurement of 

Impedance at High Power Level (Memorandum for File), 
Sylvester J. Haefner, Report P35 653, CLDWll-NLL, 
Feb. 15, 1944. Div. 6-612.53-Mll 

3. Magnetostriction Transducers and High Power Super 
Sonic Pulsing, Frederick V. Hunt, Roger W. Hickman, 
Malcolm H. Hebb, Lyman N. Miller, Francis P. Bundy, 
M 01.213-171, HUSL, Mar. 4, 1944. Div. 6-632.01-M4 

4. Non-Linear Magnetostrictive Equations, Magnetostrirtive 

Transducer at High Power, Malcolm H. Hebt), M 01.213- 
175, HUSL, Mar. 23, 1944. Div. 6-612.22-M13 

0 . Preliminary Results on High Level Pulsing of a Single 
SPEP Element, Roger W. Hickman, M 01.213-239, 
HUSL, Sept. 25, 1944. Div. 6-612.716-M15 

6. Some Observations on the Effect of Current Amplitude and 

Temperature on the Characteristics of a Single SPEP 
Element (MINI-SPEP), Roger W. Hickman, M 01.213- 
287, HUSL, Nov. 29, 1944. Div. 6-612.716-M19 

7. Reversible Permeability and Hysteresis Loss in Oxide- 
Annealed [Grade] A Nickel Polarized at Bo = 

S. T. Pan, M 113.5-180, HUSL, Dec. 12, 1944. 

Div. 6-612.41-M22 

8. “Wirksame Permeabilitat und Eisenverlust in Blechen 
und Drahten bei Schwachen Magnctischen Feldern,” 
\V. Cauer, Archive fi'ir Electrotechnick, Vol. 15, 1925-6, 
p. 308. 


9. Dynamic Study of Magnetostriction,” K. C. Black, 
Proceedings of the American Academy of Arts and 
Sciences, Vol. 53, No. 2, 1928. 

10. “Magnetostriction Oscillators,” G. W. Pierce, Proceed¬ 
ings of the American Academy of Arts and Sciences, Vol. 
63, 1928, ]). 1. 

11. “The Kcpiivalent Circuit of the Magnctostricti(ni Oscil¬ 
lator,” S. Butterworth, F. D. Smith, The Proceedings of 
the Physical Society, London, Eng. Vol. 43, 1931, p. 166. 

12. Fairlie Magnetostriction Reports, F. D. Smith, HUSL 
File B[ritish 10], 1931. 

13. “Magnetic Measurements at Low Flux Densities Using 
the A-C Bridge,” Victor E. Legg, Bell System Technical 
Journal, Vol. 15, 1936, p. 39. 

14. “Operating Characteristics of Power Tubes,” L. 
Chaffee, Journal of Applied Physics, Vol. 9, 1938, j). 471. 

15. “An Improved Magnetostriction Oscillator,” W. W. 
Salisbury, C. W. Porter, The Review of Scientific Instru¬ 
ments, Vol. 10, 1939, pp. 142-146. 

16. “The Characteristics of the Negative Resistance 
Magnetron Oscillator,” H. Chang, PI. L. Chaffee, 
Proceedings of the Institute of Radio Engineers, Vol. 28, 
1940, p. 519. 

17. “Power Tube Performance in Class C Am])lifiers and 
P'requency Multipliers as Influenced by Harmonic 
Voltage,” R. Sarbacher, Proceedings of the Institute of 
Radio Engineers, Vol. 31, 1943, p. 607. 


Chapter 12 


1. Harmonic Operation of Standard Projectors, PYederick V. 
Hunt, M 01.12-30, HUSL, June 23, 1943. 

Div. 6-612.23-Ml 

2. Nickel Alloys for Transducers, P’rederick V. Hunt, 
M 113.50-39, HUSL, July 30, 1943. Div. 6-612.41-M4 

3. Visit to West Lynn Laboratory of General Electric re¬ 
garding Materials for Permanent Magnets, P’rancis P. 
Bundy, M 113.50-59, HUSL, Sept. 25, 1943. 

Div. 6-612.42-M2 

4. General Ideas on Permanent Magnet Polarization of 

Magnetostrictive Transducers, Francis P. Bundy, M 01.- 
213-82, HUSL, Sept. 29, 1943. Div. 6-612.1-M3 

5. Permanent Magnet Polarization of Laminated MS Trans¬ 
ducer Elements by Use of Bimetallic Sheets, Specific Ap¬ 
plication to No. 2 Sonar Elements, P'rancis P. Bundy, 
M 01.213-94, HUSL, Oct. 14, 1943. Div. 6-612.1-M5 

6. Blister Rubber Paint, P'rancis P. Bundy, M 113.50-74, 

HUSL, Nov. 9, 1943. Div. 6-612.44-M5 

7. Thoughts on Design of Transducers for an SO kc Sonar 

System, P'rancis P. Bundy, M 02.453-49, HUSL, Dec. 7, 
1943. Div. 6-612.71-M18 


8. Rubber for Underwater Use, Alan H. Selker, M 113.50- 

109, HUSL, Mar. 31, 1944. Div. 6-612.43-M3 

9. Sonar Transducer Proposals, John D. Lane, M 02.45-165, 

HUSL, Apr. 4, 1944. Div. 6-612.71-M25 

10. Suggested Tests of Acoustical Transparency and Damping 
of Rubber and Rubber Substitutes, P'rancis P. Bundy, 
M 01.21-70, HUSL, May 2, 1944. Div. 6-612.43-M4 

11. Stepped Frequency Transducers, G. W. Renner, Francis 
P. Bundy, M 01.223-90, HUSL, May 4, 1944. 

Div. 6-612.71-M27 

12. Measurement of Reflection Coefficient, Malcolm H. Hebb, 
Nelson M. Blachman, HUSL, May 19, 1944. 

Div. 6-612.51-M9 

13. Compressed Metallic Dust as a Magnetostrictive Material, 

William T. Bartholomew, P'rancis P. Bundy, M 113.5- 
147, HUSL, July 7, 1944. Div. 6-612.42-M8 

14. Task No. jB, Modification of QC-Type Projector (Finid 
Report), Section 6.67, U. S. Navy BuShips, Sonar De¬ 
velopment Contract NN sr-46932 with Western Electric 
Co., Inc., BTL, Dec. 1, 1944. 


CONFIDENTIAL 



BIBLlOGKArilV 


173 


('hapler 13 


1. Liquid within Dome, Addition of Aerosol, Hayward W. 
Henderson, M 01.12-21, HUSL, .\pr. 22, 1943. 

Div. 6-612.44-Ml 

2. Properties and Uses of Alnico Magnets, Kenneth X. 

P'romin, Francis P. Bundy, M 01.213-35, HUSL, .Apr. 

23,1943. Div. 6-612.42-Ml 

3. The pc Rubber, Francis P. Bundy, M 113.50-25, HUSL, 

June 10, 1943. Div. 6-612.43-Ml 

4. Harmonic Operation of Standard Projectors, Frederick V. 

Hunt, M 01.12-30, HUSL, June 23, 1943. 

Div. 6-612.23-Ml 

5. Transducer Cable Shield with Conducting Rubber, H. IL 
Stewart, M 113-52, HUSL, July 13, 1943. 

Div. 6-612.43-M2 

6. Sonar MS Transducer, Frederick V. Hunt, M 02.45-54, 

HUSL, July 14, 1943. Div. 6-612.711-Ml 

7. Transducer Diaphragms, Fred H. Smith, M 01.221-22, 

HUSL, July 14, 1943. Div. 6-612.8-M3 

8. Interlaced Transducer for Sonar, J. Lewis Hathaway, 
M 02.452.20-30, HUSL, July 15, 1943. 

Div. 6-612.71-MlO 

9. The Problem of Sonar Transducers, Roderic M. Scott, 
M 02.45-56, HUSL, July 17, 1943. Div. 6-612.711-M2 

10. Interleaved Transducer for Sonar, San Diego Echo Re¬ 

peaters, Roderic M. Scott, M 02.45-57, HUSL, July 21, 
1943. Div. 6-612.71-Mll 

11. Reduction of Eddy Currents in Magnetostrictive Tubes, 
Malcolm H. Hehh, M 01.213-62, HUSL, July 24, 1943. 

Div. 6-612.8-M4 

12. Lamination for Model d Sonar Transducer, Malcolm H. 
Hehh, M 02.452.20-38, HUSL, July 30, 1943. 

Div. 6-612.712-Ml 

13. Line Source Transducer and Possible Sonar Application, 
Roland K. Mueser, M 02.45-70, HUSL, July 30, 1943. 

Div. 6-612.62-M12 

14. 7'he No. 2 Sonar Transducer Element, Fd-ancis P. Bund}’, 
M 02.4.5-84, HUSL, Sept. 10, 1943. Div. 6-612.712-M2 

15. Sonar, Test and Analysis of Laminated Transducer Ele¬ 
ment, James W. Follin, Jr., Rohei't .A. Payne, Malcolm 
H. Hehh, M 02.45-87, HUSL, Sept. 17, 1943. 

Div. 6-612.71-M12 

16. Cyclewetd, Francis P. Bundy, M 110.10-37, HUSL, 

Sept. 18, 1943. Div. 6-612.44-M2 

17. Visit to HV.st Lynn Laboratory of General Electric re¬ 
garding Materials for Permanent Magnets, Francis P. 
Bundy, M 113..50-.59, HUSI., Sept. 25, 1943. 

Div. 6-612.42-M2 

18. General Ideas on Permanent Magnet Polarization of 

Magnetostrictive Transducers, Francis P. Bundy, M 01.- 
213-82, HUSL, Sept. 29, 1943. Div. 6-612.1-M3 

19. Permanent Magnet Polarization of Magnetostrictive Sonar 

Transducer, Francis P. Bundy, M 02.45-90, HUSL, 
Oct. 4, 1943. Div. 6-612.1-M4 

20. I'ests on Some New DuPont Adhesives, G. W. Renner, 
M 113.50-62, HUSL, Oct. 4, 1943. Div. 6-612.44-M3 

21. Tests on Model No. 2 Sonar Transducer, James W. Follin, 


Jr., Malcolm H. Hehh, M 02.45.70-35, HUSL, Oct. 7, 
1943. Div. 6-612.712-M3 

22. Permanent Magnet Polarization of Laminated MS Trans¬ 
ducer Eleynents by Use of Bimetallic Sheets, Specific .Ap¬ 
plication to No. 2 Sonar Elements, Francis P. Bundy, 
M 01.213-94, HUSL, Oct. 14, 1943. Div. 6-612.1-M5 

23. Pattern Requirements for Sonar Transducer, Malcolm H. 
Hehh, M 02.45.70-38, HUSL, Oct. 15, 1943. 

Div. 6-612.21-M7 

24. Transducers, Thoughts on Laminated, Frederick V. Hunt, 
M 01.213-101, HUSL, Oct. 25, 1943. 

Div. 6-612.71-M15 

25. Transducers, Thoughts on Laminated, Eric .A. Walker, 
M 01.213-102, HUSL, Oct. 25, 1943. 

Div. 6-612.71-M14 

26. Laminated Transducers, Further Thoughts on, Francis P. 
Bundy, M 01.213-104, HUSL, Xov. 2, 1943. 

Div. 6-612.71-M16 

27. Millerphone, John D. Lane, M 01.213-105, HUSL, 

Xov. 2, 1943. Div. 6-612.8-MlO 

28. Blister Rubber Paint, Francis P. Bundy, M 113.50-74, 

HUSL, Xov. 9, 1943. Div. 6-612.44-M5 

29. Sonar Transducer. Certain Measurements and Recom¬ 

mendations, F. Burton Jones, M 02.45.70-48, HUSL, 
Xov. 16, 1943. Div. 6-612.71-M17 

30. Thoughts on Design of Transducers for an 80 kc Sonar 

System, Francis P. Bundy, M 02.453-49, HUSL, Dec. 7, 
1943. Div. 6-612.71-M18 

31. Millerphone, Casketphone, John D. Lane, J. O. Xatwick, 
M 01.213-127, HUSL, Dec. 10, 1943. 

Div. 6-612.8-M12 

32. Remarks on iSugyested Design of Transducers for High- 

Frequency Sonar Systems, Roderic M. Scott, M 02.453-52, 
HUSL, Dec. 11, 1943. Div. 6-612.71-M19 

33. .Ansivers to Questions in Scott’s Memorandum of Dec. 11 
[1943] regarding High Frequency Sonar Transducers, 
Francis P. Bundy, M 02.453-55, HUSL, Dec. 15, 1943. 

Div. 6-612.71-M20 

34. Results of Comparison Tests on Campbell and Murphy 

10 mil 2" Stacks, Thomas P. Merritt, M 01.213-145, 
HUSL, Feh. 1, 1944. Div. 6-612.712-M4 

35. Millerphone [Xo.] H Report, John D. Lane, M 01.213- 

166, HUSL, Feh. 29, 1944. Div. 6-612.8-M13 

36. The Vertical Pattern of a Split Sonar Element, Malcolm 

H. Hehh, Xelson M. Blachman, M 01.21-56, HUSL, 
Mar. 1, 1944. Div. 6-612.21-M13 

37. Coupling Tests on Segmented and Unsegmented Ladder- 

phone Starks, LDPI No. 1 and No. 2, William T. 
Bartholomew, Francis P. Bundy, M 01.213-173, HUSL, 
Mar. 16, 1944. Div. 6-612.31-M8 

38. Rubber for Underwater Use, .A. H. Selker, M 113.50-109, 

HUSL, Mar. 31, 1944. Div. 6-612.43-M3 

39. Sonar Transducer Proposals, John D. Lane, M 02.45-165, 

HUSL, .Ai)r. 4, 1944. Div. 6-612.71-M25 

40. Preliminary Survey of the .Analysis of the Impedance and 
.Admittance Data on the HP-\\ Starks, Robert E. Payne, 
M 02.45.7-73, HUSL, A])!’. 6, 1944. Div. 6-612.55-M14 


CONFIDENTIAL 



474 


hibli(k;rapiiv 


41. Results of the Analysis of (he Admittance Data on the 
Individual HP-\ \ Stacks, including the Selection and *4;- 
rangement of the Elements in HP-ll No. IB, Robert E. 
Payne, M 02.45.7-78, IIUSL, Apr. 13, 1944. 

Div. 6-G12.55-M15 

42. Si?igle Element Pattern of Cylindrical Transducer, Gerald 
I. Harrison, M 01.21-68, HUSL, Apr. 28, 1944. 

Div. 6-612.21-M16 

43. Suggested Tests of Acoustical Transparency and Damping 
of Rubber and Rubber Substitutes, Francis P. Biindy, 
M 01.21-70, HUSL, May 2, 1944. Div. 6-612.43-M4 

44. Tests on 2" HP-2 Stacks, Thomas P. Merritt, Francis P. 
Bundy, M 02.45.7-87, Hl’SL, May 3, 1944. 

Div. 6-612.712-M7 

45. Transducers Separated from the IFatcr by Rubber or Oil, 
Nelson M. Blachman, M 01.21-72, HUSL, May 12, 1944. 

Div. 6-612.43-M6 

46. Appearance of 9(f Minor Lobes in Scanning Sonar 
Transducer Patterns, Thom:is P. Merritt, Francis P. 
Bundy, M 02.45.7-S)0, HUSL, May 13, 1944. 

Div. 6-632.61-M2 

47. Transmission Loss in Natural and Synthetic Rubbers, 
Paul E. Sabine, M 113.5-130, HUSL, May 24, 1944. 

Div. 6-612.43-M8 

48. Lamination Design to Minimize the Q, Nelson M. Blach¬ 
man, M 01.213-200, HUSL, .June 17, 1944. 

Div. 6-612.34-M6 

49. QH Sonar, Depression of Beam, Malcolm H. Hebb, 
M 02.4.5-195, HUST., .June 19, 1944. Div. 6-612.714-Ml 

50. Sonar-Lamination Dimensions as Functions of the 

Number of Sections, Nelson M. Blachman, M 01.213-203, 
HUSL, .June 26, 1944. Div. 6-612.71-M28 

51. Compressed Metallic Dust as a Magnetostrictive Material, 

William T. Bartholomew, hhancis P. Bundy, M 113.5- 
147, HUSI., .July 7, 1944. Div. 6-612.42-M8 

52. Transducer Nomenclature [Part] No. II, C. E. Hesthal, 
M 01.20-50, HUSL, Aug. 24, 1944. Div. 6-612.71-M30 

53. Capacitive Commutators, F. Burton Jones, Reubin H. 
Wallace, M 02.452-86, HUSL, Oct. 5, 1!)44. 

Div. 6-612.713-M7 

54. Dome for Ultimate Sonar Transducer, H. E. Harlow, 
M 02.302-32, HUSL, Nov. 3, 1944. Div. 6-612.714-M5 

.55. Pattern of a Sector of a Cylinder, Gerald I. Harrison, 
M 01.21-107, HUSL, Nov. 14, 1944. Div. 6-612.21-M22 

56. Single Element Scanning Sonar Patterns, Gerald 1. Har¬ 
rison, M 02.45.7-143, HUSL, Nov. 24, 1944. 

Div. 6-632.61-M3 

57. IJ’atcr Seal for lOO-Conductor Sonar Cable, Alan H. 
Selker, M 110.1-163, HUSI., Dec. 6, 1944. 

Div. 6-612.714-M6 

58. Construction and First Tests of the Magnetostrictive Scan¬ 
ning Sonar Transducer HP-3DS, RoJ)ert B. Watson, 
Francis P. Bundy, M 02..502-6, HUSL, Dec. 13, 1944. 

Div. 6-612.713-M9 

59. A Detailed Study of Sintered-Oxide Magnets in HP-3 
Stacks, Milton R. Carlson, S. T. Pan, Francis P. Bundy, 
M 01.213-285, HUSL, Dec. 15, 1944. 

Div. 6-612.42-Mll 

60. Submarine Bottom Side Transducer, H. E. Harlow, 
M 02.4.53.2-116, HUSL, Jan. 4, 1945. 

Div. 6-612.71-M32 


61. Pattern of a 27U° Sector, Gerald 1. Harrison, M 01.21-109, 

HUSI., Jan. 5, 1945. Div. 6-612.21-M26 

62. Trip to Bell Telephone Laboratories on the Question of 

HP-S Cable, H. E. Harlow, M 02..502-10, HUSL, 
Jan. 1.5, 1945. Div. 6-612.715-M2 

63. Theoretical Scanning Sonar Patterns, Gerald I. Harrison, 
M 02.45.1-22, HUSL, Jan. 19, 1945. Div. 6-632.61-M4 

64. Pattern of a 27U° Sector {Corrected), Gerald I. Harrison, 
M 01.21-113, HUSI., .Jan. 26, 1945. Div. 6-612.21-M28 

65. The BTL BD-Pair Cable, H. E. Harlow, M 02.,502.16, 

HUSL, Feb. 7, 194.5. Div. 6-612.71.5-M4 

66. Present Bad Terminology relating to Diameter of Scanning 

Transducers, Malcolm H. Hebb, M 02.45.2-194, HUSIj, 
I<>b. 8, 1945. Div. 6-612.71-M33 

67. Directional Transmission for Depth Scanning, Frederick 
V. Hunt, M 02.502-20, HUSL, I->b. 15, 1945. 

Div. 6-612.715-M7 

68. Pattern of 270° and 90° Sectors {Really Correct), Gerald I. 
Harrison, M 01.21-115, HUSL, h'eb. 26, 1945. 

Div. 6-612.21-M30 

ti9. Te.sts of the Partially Complete Sangamo XQHA System 
at the HUSL Barge, Francis P. Bundy, M 02.45.7-158, 
HUSL, Mar. 1, 1945. Div. 6-632.222-Ml 

70. Technical Literature for Indoctrination of Prospective 
Manufacturers of QH Sonar Transducers, hh'ancis P. 
Bundy, M 02.45.3-102, HUSL, Mar. 6, 1945. 

Div. 6-612.71-M34 

71. Method for Sealing Collyer 50-Pair Flexible, Blocked Cable, 
Alan H. Selker, M 02.502-36, HUSL, Mar. 9, 1945. 

Div. 6-612.715-M9 

72. Scanning Sonar, Directional Transmitting Beam for, 
I'hederick V. Hunt, M 02.502-38, HJ’SI^, Mar. 17, 1945. 

Div. 6-612.21-M31 

73. Turkshead Covering for HP-3S, C. I'h Hesthal, M 02.- 
453.2-142, HUSL, Mar. 19, 1945. Div. 6-612.713-M 13 

74. Study of Difference between Commutators I and 2 of the 

Depth Scanning System, Robert H. Hughes, M 02.507-28, 
HUSL, Mar. 23, 1945. Div. 6-612.715-M 10 

75. Total Attenuation Patterns, Gerald I. Harrison, M 01.21- 

119, IH^SL, Mar. 24, 1945. Div. 6-612.21-M32 

76. Transmission Pattern for Constant Echo Strength, Gerald 
I. Harri.son, M 01.75-15, HUSL, Mar. 26, 1945. 

Div. 6-612.21-M33 

77. Recommendations on Attenuation and Lag Lines for the 

Sangamo XQHA System, Gerald J. Harrison, M 01.21- 
126, HUSL, Apr. 2, 1945. Div. 6-632.221-M4 

78. Repair of HP-3DS No. 1 Transducer, N. H. Godbold, 
M 02.502-41, HUSL, Apr. 5, 1945. Div. 6-612.713-M15 

79. Sound Attenuation in Coating Materials, Alan H. Selker, 
G. W. Renner, M 01.21-128, HUSL, Apr. 9, 1945. 

Div. 6-612.43-M16 

80. Oil Filling of Transducers, Alan H. Selker, M 01.213-324, 

HlhSL, Apr. 10, 1945. Div. 6-612.44-M13 

81. Cable for Ultimate Type B and Submarine Syste?ns, 
Rol)ert B. Watson, M 02.502-43, HI^SJj, Apr. 12, 1945. 

Div. 6-632.421-M17 

82. Design B for Scanning Sonar XQHA, Gerald I. Harrison, 
M 02.45.1-26, HUSI., Apr. 14, 1945. 

Div. 6-632.221-M6 

83. Theoretical Scanning Sonar Patterns, Gerald I. Harrison, 
M 02.45.1-29, HUSI>, Ai.r. 16, 1945. Div. 6-632.61-M7 


CONFIDENTIAL 



BIBLIOGRAPHY 


475 


84. Organic Cements m Underwater Sound Apparatus, Alan 
H. Selker, M 113.5-185, HUSL, Apr. 18, 1945. 

Div. 6-612.44-M14 

85. Further Subdivision of Scanning Rotor to Achieve More 

Uniform Rotation of Beam, Malcolm H. Hebb, M 02.- 
45.1-31, HUSL, Apr. 19, 1945. Div. 6-632.61-M8 

86. Scanning Sonar Transducer Cable, 11. PI. Harlow, 
M 02.45.2-204, HUSL, May 11, 1945. Div. 6-632.53-M6 

87. Some Applications of Organic Plastics and Rubber in 
Underwater Sound Apparatus, Alan H. Selker, M 113.5- 


191, HUSL, May 26, 1945. Div. 6-612.43-M17 

88. Construction and First Tests of Magnetostrictive Scanning 
Sonar Transducer HP-SD No. 2, Leon W. Camp, 
Robert B. Watson, M 02.502-50, HUSL, July 3, 1945. 

Div. 6-632.51-M9 

89. Bearing Deviation Indicator (Completion Report), OSRD 
6425, NDRC 6.1-sr287-2075, HUSL, Nov. 1, 1945. 

Div. 6-631.4-Ml 

90. Scanning Sonar, Summary Technical Report, NDRC 
Division 6, Volume 16. 


Chapter 14 


1. Tests on the Hebbphone, Roderic M. Scott, M 01.213-33, 

HUSL, Mar. 18, 1943. Div. 6-612.71-M7 

2. Change of Resistance to Ground of the 36-Element Trans¬ 

ducer, Roderic M. Scott, M 02.452.70-24, HUSL, July 
23, 1943. Div. 6-612.711-M3 

3. Cycleweld, PTancis P. Bundy, M 110.10-37, HPTSL, Sept. 

18, 1943. Div. 6-612.44-M2 

4. Tests on Model No. 2 Sonar Transducer, James W. P'ollin, 

Jr., Malcolm H. Hebb, M 02.45.70-35, HUSL, Oct. 7, 
1943. Div. 6-612.712-M3 

5. Millerphone, John D. Lane, M 01.213-105, HP^SL, Nov. 

2,1943. Div. 6-612.8-MlO 

6. Millerphone, Casketphone, John D. Lane, J. O. Natwick, 

M 01.213-127, HUSL, Dec. 10, 1943. 

Div. 6-612.8-M12 

7. Tests on the 36-Element Hebbphone I Transducer, Thomas 
P. Merritt, Harold P. Knauss, Arthur C. Clatfelter, 
M 02.45.70-56, HUSL, Dec. 30, 1943. 

Div. 6-612.711-M4 

8. Results of Comparison Tests on Campbell and Murphy 

10 Mil 2" Stacks, Thomas P. Merritt, M 01.213-145, 
HUSL, P>b. 1, 1944. Div. 6-612.712 M4 

9. Millerphone, [No.] II Report, John D. Lane, M 01.213- 

166, HUSL, P'eb. 29, 1944. Div. 6-612.8 M13 

10. Performance of HP-2 [No.] 1 on USS Sardonyx, C. E. 
Hesthal, M 02.45.4-50, HUSL, Mar. 4, 1944. 

Div. 6-612.712-M5 

11. Construction and First Tests of the HP-2 [No.] 1 Trans¬ 

ducer, P^rancis P. Bundy, C. Pi. Hesthal, Thomas P. 
Merritt, Arthur Clatfelter, M 02.45-161, HPTSL, Mar. 
21, 1944. Div. 6-612.712-M6 

12. Proposed Tests for HP-1 Transducer, Francis P. Bundy, 
M 02.45.7-71, HUSL, Mar. 27, 1944. Div. 6-612.711-M5 

13. Preliminary Survey of the Analysis of the Impedance and 
Admittance Data on the HP-ll Stacks, Robert E. Payne, 
M 02.45.7-73, HPTSL, Apr. 6, 1944. Div. 6-612.55-M14 

14. Results of the Analysis of the Admittance Data on the 
Individual HP-\\ Stacks, including the Selection and 
Arrangement of the Elements in HP-\\, No. IB, Robert 
E. Payne, M 02.45.7-78, PIPTSL, Apr. 13, 1944. 

Div. 6-612.55-M15 

15. Handling Equipment for Cleaning, Annealing, and Coat¬ 

ing Nickel Laminations, Paul Pi. Sabine, M 110.10-127, 
HPTSL, Apr. 20, 1944. Div. 6-612.41-M18 


16. That Which Is Rotten with HP-1, Stanley R. Rich, David 
C. Whitmarsh, M 02.45.7-82, HP^, Apr. 21, 1944. 

Div. 6-612.711-M6 

17. Comparison Tests on Hebbphone 1 and Hebbphone 2, 

Thomas P. Merritt, Francis P. Bundy, F. Burton Jones, 
.Arthur C. Clatfelter, C. H. Hesthal, M 02.45.7-85, 
HPTSL, May 2, 1944. Div. 6-612.711-M7 

18. Tests on 2" HP-2 Slacks, Thomas P. Merritt, P^rancis P. 
Bundy, M 02.45.7-87, HUSL, May 3, 1944. 

Div. 6-612.712-M7 

19. Miracle Adhesives, Francis P. Bundy, Leon W. Camp, 
M 113.5-127, HUSL, May 18, 1944. Div. 6-612.44-MlO 

20. Assembly of HP-3 Stacks, Leon W. Camp, M 02.453.2-45, 

HUSL, July 13, 1944. Div. 6-612.713-Ml 

21. Consolidation of HP-3 Laminations, Leon W. Camp, 
M 02.453.2-47, HPTSL, July 15, 1944. 

Div. 6-612.713-M2 

22. Assembly of HP-3 Stacks, Supplementary Mewo[randum] 

of July 13 [1944], Leon W. Camp, M 02.453.2-48, 
HUSL, July 24, 1944. Div. 6-612.713-M3 

23. Consolidation of Nickel Laminations, Leon W. Camp, 
M 02.453.2-49, HUSL, July 26, 1944. Div. 6-612.44-Mll 

24. Construction and Testing of HP-5 Transducer Stacks at the 
Sangamo Electric Company, Francis P. Bundy, James J. 
Faran, Jr., M 02.4.5-208, HUSL, Aug. 21, 1944. 

Div. 6-612.714-M2 

25. Specifications for Consolidation and Winding of Lamina¬ 

tions, Leon W. Camp, M 02.453.2-52, HUSL, Aug. 24, 
1944. Div. 6-612.713-M4 

26. Transducer Nomenclature [Part] No. II, C. E. Hesthal, 
M 01.20-50, HP'SL, Atig. 24, 1944. Div. 6-612.71-M30 

27. Harvey Radio [Laboratories’] First HP-2 Stack, Francis 
P. Bundy, M 02.45.7-99, HPTSL, Sept. 6, 1944. 

Div. 6-612.713-M5 

28. Tests on 5 Sangamo HP-5 Transducer Stacks, Francis P. 
Bundy, M 02.45.7-101, HPTSL, Sept. 8, 1944. 

Div. 6-612.714-M3 

29. Transmission Directivity Indices of Hebbphone 1, Hebb¬ 
phone 2-B and Other Similar Hydrophones, P\ Burton 
Jones, M 02.45.7-109, HUSL, Sept. 21, 1944. 

Div. 6-612.711-M8 

30. Impedance of HP-3 Stacks, Francis P. Bundy, M 02.50- 

116, HPTSL, Oct. 5, 1944. Div. 6-612.713-M6 


CONFIDENTIAL 




476 


BIBLIOGRAPHY 


31. Aroustir Patterns of the HP-2B Scanning Sonar Trans¬ 

ducer on the USS Cythera, Harold P. Knauss, A. H. 
Powers, Francis P. Bundy, M 02.45.7-114, HUSL, 
Oct. 10, 1944. Div. 6-612.712-M8 

32. Tests on 6 Sangamo HP-5 Transducer Stacks, FrancLs P. 
Bundy, M 02.45.7-117, HUSL, Oct. 14, 1944. 

Div. 6-612.714-M4 

33. Cycle-Welding of HP-3 Stacks, Paul E. Sabine, M 02.45.2- 

129, HUSL, Oct. 28, 1944. Div. 6-612.713-M8 

34. HP-8 Laminations in the Light of our HP-3 Experience, 
Paul E. Sabine, M 02.45.2-113, HUSL, Nov. 1, 1944. 

Div. 6-612.715-Ml 

35. Lamination Cleaning, Jack C. Cotton, M 110.1-158, 

HUSL, Dec. 1, 1944. Div. 6-612.71-M31 

36. Water Seal for lOO-Conductor Sonar Cable, Alan H. Selker, 
M 110.1-163, HUSL, Dec. 6, 1944. Div. 6-612.714-M6 

37. Construction and First Tests of the Magnetostrictive 
Scanning Sonar Transducer HP-3DS, Robert B. Watson, 
Francis P. Bundy, M 02.502-6, Hl"SL, Dec. 13, 1944. 

Div. 6-612.713-M9 

38. HP-3 Stacks Submitted by Harvey Radio Corporation, 
I>eon W. Camp, M 02.45.7-149, HUSL, Dec. 29, 1944. 

Div. 6-612.713-MlO 

39. Plans for Testing HP-5 Sangamo Assembly at Barge, 
Francis P. Bundy, M 02.45.4-132, HUSL, Jan. 17, 1945. 

Div. 6-612.714-M7 

40. HP-8 Laminated Stacks, Leon W. Camp, M 01.213-302, 

HUSL, Feb. 5, 1945. Div. 6-612.715-M3 

41. Cleaning and Consolidation of HP-8 Laminations, Leon 
W. Camp, M 02.45.2-193, HUSI., Feb. 8, 1945. 

Div. 6-612.715-M5 

42. Tentative Schedule of Measurements on 26 kc Depth 
Scanning System Aboard CSSCythera, Robert B. Watson, 
M 02.507-10, HUSL, Feb. 14, 1945. Div. 6-612.715-M6 

43. Directional Transmission for Depth Scanning, Frederick 
V. Hunt, M 02.502-20, HUSL, Feb. 15, 1945. 

Div. 6-612.715-M7 

44. Final Tests on Sangamo HP-5 No. 1 Transducer before 

Installation on the Galaxy, P^rancis P. Bundy, M 02.45.4- 
135, HUSL, Feb. 27, 1945. Div. 6-612.714-M8 

45. Tests of the Partially Complete Sangamo XQHA System 

at the Hl^SL Barge, P'rancis P. Bundy, M 02.45.7-158, 
HUSL, Mar. 1, 1945. Div. 6-632.222-Ml 

46. Measurements on HP-SDS as Installed on I'SS Cythera, 


Robert B. Watson, M 02.507-21, HUSL, Mar. 3, 1945. 

Div. 6-612.713-Mll 

47. Measurements of Depth Scanning System on (ISS Cythera, 
Robert B. Watson, M 02.507-22, HUSL, Mar. 8, 1945. 

Div. 6-612.715-M8 

48. Tests on Sangamo HP-5 No. 3 Transducer, C. Pk Hesthal, 
P’rancis P. Bundy, M 02.45.7-159, HUSI>, Mar. 9, 1945. 

Div. 6-612.714-M9 

49. Measurements on HP-3DS as Installed on CSS Cythera, 
Robert B. Watson, M 02.507-23, HUSL, Mar. 10, 1945. 

Div. 6-612.713-M12 

50. Tests on Sangamo HP-5 No. .( Transducer, Ray Rast, 
P’rancis P. Bundy, M 02.45.7-161, HUSL, Mar. 22, 1945. 

Div. 6-612.714-M10 

51. Outline of Tests Suggested for HP-3, P'rancis P. Bundy, 
M 02.45.7-162, HUSL, Mar. 24, 1945. 

Div. 6-612.713-M14 

52. Addendum to A/cwo[randum] of March !), U),(t5, Entitled, 

“Tests of Sangamo HP-5 No. 3 Transducer,” C. E. 
Hesthal, P'rancis P. Bundy, M 02.45.7-160, HUSL, 
Mar. 26, 1945. Div. 6-612.714-M 11 

53. Recommendations on Attenuation and Lay Lines for the 

Sangamo XQHA System, Gerald 1. Harrison, M 01.21- 
126, HUSL, Apr. 2, 1945. Div. 6-632.221-M4 

54. Tests of Sangamo HP-5 No. 5 Transducer, Jack C. Cotton, 
M 02.45.7-172, HUSI., May 7, 1945. 

Div. 6-612.714-M 12 

.55. Program of Tests for HP-8D No. 2 at Barge, I.,eon W. 
Camp, Robert B. Watson, Francis P. Bundy, M 02.- 
507-32, HUSL, May 8, 1945. Div. 6-612.71.5-Mll 
.56. Tests of HP-3 No. 1 Transducer, M. J. P'oral, P’rancis P. 
Bundy, M 02.45.7-174, HUSL, May 23, 1945. 

Div. 6-612.713-M16 

.57. Construction and First Te.sts of Magnetostrictive Scanning 
Sonar Transducer, HP-8D No. 2, Leon W. Camp, 
Robert B. Watson, M 02..502-.50, HUSL, July 3, 1945. 

Div. 6-632.51-M9 

58. Scanning Sonar, Summary Technical Report, NDRC 
Division 6, Vol. 16, Chap. 5. 

.58a. Ibid., Chap. 6. 

59. Task No. -iB Modification of QC-Type Projector (P'inal 
Report), Section 6.67, IL S. Navy BuShips, Sonar 
Development Contnict NX sr-46932 with Western 
Electric Co., Inc., BTI>, Dec. 1, 1944. 


CONFIDENTIAL 



CONTRACT numbers, CONTRACTORS, AND SUBJECT OF CONTRACTS FOR DIVISION 6 


Contract Number 

Name and Address of Contractor 

Subject 

OEMsr-20 

The Trustees of Columbia University in the 
City of New York, New York, N. Y. 

Studies and experimental investigations in 
connection with and for the development of 
equipment and methods pertaining to sub¬ 
marine warfare 

OEMsir-1128 

The Trustees of Columbia University in the 
City of New York, New York, N. Y. 

Conduct studies and experimental investiga¬ 
tions in connection with and for the devel¬ 
opment of equipment and methods involved 
in submarine and subsurface warfare 

OEMsr-287 

President and Fellows of Harvard College, 
Cambridge, Massachusetts 

Studies and experimental investigations in 
connection with (i) the development of 
equipment and devices relating to subsur¬ 
face warfare. 

OEMsr-346 

Western Electric Company, Inc., New York, 
N. Y. 

Studies and experimental investigations in 
connection with submarine and subsurface 
warfare 

OEMsr-78.5 

Western Electric Company, Inc., New York, 
N. Y. 

Studies and experimental investigations in 
connection with Project 61 


CONFIDENTIAL 


477 








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INDEX 


The subject indexes of all STR volumes are combined in a master index printed in a separate volume. For access 
to the index volume consult the Army or Navy Agency listed on the reverse of the half-title page. 


.\ nickel, properties, 65-104 
composition, 65 

dependence of remanence on anneal¬ 
ing temperature, 78 
effect of annealing on magnetic 
properties, 72 

effect of grain orientation on mag¬ 
netic properties, 74 
effect of temperature on magnetic 
properties, 101-104 
magnetic strain curves, 83 
magnetostrictive constant, 89 
maximum coercive force, 75 
normal magnetization curve, 67 
resistivity, 93 
reversible permeability, 88 
uniformity of stock, 74 
Young’s modulus when magnetized, 
93 

.\bsolute calibration of hydrophones, 
311 

.\bsorbing screens, acoustic, 322 
.\coustic axis of transducer, definition, 
14 

.\coustic contact between water and 
transducer, 279, 391 
Acoustic impedance 

see Radiation impedance 
Acoustic intensity, effect of cavitation, 
324 

.\coustic loading 

on inside of ring t ransducei', 172 
radially vibrating transducer, 140 
.\coustic patterns of transducers 
see Directivity patterns, theoretical 
Acoustic pressure, maximum obtainable 
from magnetostriction, 9 
Acoustic resistance, definition, 13 
Active face of transducer, design, 374- 
375 

.\diabatic magnetostriction coefficients, 
64 

Admittance bridge, portable, 280 
Admittance diagrams 

see Impedance and admittance dia¬ 
grams 

Admittance locus plotter, 277 
.\dmittance measurement methods, 
transducer 

see Impedance measurement meth¬ 
ods, transducer 
Admittometer, 269 
Air, radiation impedance, 28 
Alnico magnets, polarizing, 151 


.\luminum faces for transducer ele¬ 
ments, 419 

.\mercoat33, water-resistant paint, 166 
.\nnealing magnetostrictive materials, 
66, 73, 141 

A.ssembly and mounting of transducers 
breakage precautions, 370 
cable design, 390 
consolidating jigs, 427 
consolidation, 162, 173 
corrosion resistance, 371 
deck mounting, 371 
facing material, 391 
horizontal mounts, 371 
HP-2 type in containers, 378 
HP-2B element as.sembly, 376 
I IP-3 as.sembly with plastic face 
strip, 378 

I IP-3 element assembly, 377 
ladderphone assembly, 381 
materials of construction, 373 
millerphone assembly, 380 
mounting methods, 157, 291, 371 
production testing, 427 
QC flange, 371 
SP-1 type in containers, 379 
spool assembly, 435 
streamlining, 392 
support materials, 373 
tolerance in location of elements, 375 
tolerance on element uniformity, 367 
tube and plate types with sealed dia¬ 
phragms, 381 
t ubular arrays, 382 
water seals, 361, 385, 436 
winding, 428 

.Asymmetrical stack transducer 9X9 
in., 202-207 

acoustic measurements, 205 
directivity patterns, 205 
laminations, 202 
polarization, 204 
sensitivity, 205 
windings, 203 

Automatic i)lotting of transducer im¬ 
pedance, 273-277 
.Axis of transducer, definition, 14 


B-6 hydrophone series, 148-150 
B-19 hydrophone, 150 
B-19A hydrophone, 150 
B-19B hydrophone, 148-151, 154 
use as a standard, 310 


B-19H hydrophone, 154-156, 382 
midget model, 156 
use as a standard, 310 
B-19K hydroj)hone, 156 
B-19L hydrophone, 156 
Baffle types, theoretical, 120 
Baffles, effect on t ransducer directivity 
patterns, 120 

Balance indicators (tuned circuits) for 
impedance bridges, 261-264 
Bandwidth of transducer 
see also Q of transducer 
definition, 20-21 
effect on directivity, 130 
effect of termination, 57 
in scanning systems, 370 
response curve me;isurement, 281- 
287, 295 

Bar and piston type laminated ele¬ 
ments 

see Laminated bar stacks 
Beam patterns 

see Directivity patterns, theoretical 
Beam-forming network, 366 
Becker and Kersten’s initial permeabil¬ 
ity formula, 73 
Bell Telephone Laboratories 
broad band magnetostriction projec¬ 
tor, 171 

cavitation studies, 324 
CI-100 transducer, 194 
electrodynamic projector. Type IK, 
308 

laminated block transducers, 200 
MKX hydrophone, 161 
MOX transducer, 193 
non-directional ring stack transducer, 
168 

QC projector studies, 231 
ring scroll hydrophone, 160 
ring transducer, 171 
survey of magnetostrictive material, 
62 

tube-and-plate transducers, 360 
W-10125 impedance bridge, 255 
Bimetal laminations, 402 
Blocked impedance of transducer, 26 
Bookiffione transducer, 187-197, 360 
acoustic measurements, 190 
multielement ty{)e, 190 
performance characteristics of ele¬ 
ments, 188 

Bostick T46M cement for laminated 
stacks, 189 


CONFIDENTIAL 


479 


180 


INDEX 


Breakage precautions for transducers, 
371 

Bridge methods for transducer imped¬ 
ance measurement, 239-207 
frequency-standard equipment, 2o7- 
201 

general discussion, 239-240 
Hl’SL admittance bridge, 2o2-2o5 
HUSL impedance bridge, 240-252 
reduction of bridge data, 204 
special frequency doubler used, 250- 
257 

special osoillatoi's used, 255 
tuned detectors used for bridge bal¬ 
ancing, 261-204 
W-10125 bridge of BTL, 255 
Broad band transducers, 171, 208-210, 
225 

Brush Model C'-13-2 crystal hydro¬ 
phone, 308 

Bubbles on transducer face, avoidance, 
200, 279, 391 

C-13-2 standard crystal hydrophone, 
308 

Cable designing, transducer, 390, 437 
Cable seals, transducer, 384 
Calibration of transducers 
measuring equipment, 297 
reciprocity method, 17-18, 311-313 
use of absorbent-lined tanks, 281-287 
Cashew-base varnish for coating trans¬ 
ducers, 165 

Castor oil filling for transducers, 163, 
438 

Cavitation limit on transducer, 324, 
374 

Cementing laminated stacks to dia- 
l)hragms, 189 

Centrifugal castings for transducer 
frames, 373 

Characteristic frequency for a mag¬ 
netic sheet, 35, 37 
Cl-50 transducer, 200 
CI-60 transducer, 200 
CI-61 transducer, 200 
CI-63 transducer, 200 
CI-64 ti'ansducer, 200 
CI-65 transducer, 200 
CI-100 transducer, 194 
Circular disk sources, directivity pat¬ 
terns, 128, 129 

Circular piston, radiation impedance, 
137 

Coatings for transducer elements, 165 
Coercive force, definition, 3 
Coercive force, variation with temper¬ 
ature, 102 

Coercivity, definition, 3 
Conductoineter, 271 
Cone hydrophones, 224 


Consolidation of laminated stacks, 162, 
173, 425 

Core impedance, transducer, 35 
Corrosion resistance of scanning trans¬ 
ducers, 371 

Corrugated tube transducer elements, 
395 

Cost of scanning transducers, 302 
Coupling between transducer sections, 
197-200 

Cunico, characteristics of, 402 
Current analogues of force, 57 
Current transmitting response, pro¬ 
jector, 295 

Cycle-weld cement for laminated 
stacks, 00, 162, 189, 425 
Cj’lindrical dipole, radiation impedance, 
136 

Cylindrical source, electrical impedance 
formulas, 39-42 

Cylindrical source, radiation imj)ed- 
ance, 130 

D nickel, properties 
composition, 05 

effect of annealing on magnetic 
properties, 75 

magnetostrictive constant, 91 
resistivity, 93 
reversible permeability, 75 
Young’s modulus when magnetized, 
93 

Decibel levels, definition, 13 
Deck mounting of transducers, 371 
Demagnetization of magnets while hot, 
409 

Demagnetizing factors of cylindrical 
rods, 07 

Demagnetizing strain, 98 
Depth angle transducers 

HP-3DkS scanning transducer, 445 
HP-8D scanning transducer, 450 
possible patterns, 368 
sword-arm, 219 
transducer mounting, 371 
Design factors for transducers 

see Scanning transducer design; 
Transducer theory 

Diaphragm as lumped impedance, 180 
Diaphragms for transducers 
magnesium, 419 
plastics, 419 

Dipole source directivity patterns, 107 
Dipole sphere, radiation impedance, 136 
Direction pattern tracer, 317 
Directivity index 

see also Directivity ratio 
definition, 138 

Directivity pattern measurement 
methods 

direction pattern tracer, 317 


measurement in absorbent-lined 
tanks, 281 

use of standard hydrophones, 297 
Directivity pattern requirements for a 
scanning transducer, 367-370 
Directivity patterns, theoretical, 105- 
138 

see also Directivity ratio 

array of point sources, 107, 108, 112 

circular disk, 128 

circular disk, clamped at edge, 129 
circular disk, shaded, 128 
designing transducers for desired pat¬ 
tern, 111-113 
dipole source, 100 
effect of baffles, 120 
effect of frequency band-width, 131 
Gaussian pattern, 111-113, 117, 123 
line sources, 113-119 
normalization, 105 
plane radiator in stiff baffle, 121-125 
point source, 100 

product theorem for line source, 110 
product tlieoremforsurface source, 125 
reciprocity theorem, 105-100 
rectangular source, 125 
relation to source strengths, 110-125 
shaded line source, 115 
split disk, phased, 129 
split square, phased, 127 
square source, 120 
Directivity ratio 

calculati(m from pattern shape, 132 
circular disk, 129 
circular disk, shaded, 129 
definition, 15, 138 
dipole source, 106, 107 
importance for listening devices, 141 
line of ))oint sources, 110 
line source, 114 
rectangular source, 128 
shaded line source, 115 
use in calculating transducer effi¬ 
ciency, 443 
Domains, magnetic, 1 
Domes, elimination of, 362 
Dynamic magnetostriction measure¬ 
ments, 69, 84 

Eddy current losses in transducers 
complex eddy current factor, 35 
curved sheets, 35 
eddy current parameter, 326 
laminated cores, 35-38, 350 
polarizing magnets, 236 
Effective area of transducer, 00 
Efficiency of four terminal network, 22, 
24 

Efficiency of transducers 

see also filddy current losses in trans¬ 
ducers; Electromechanical cou- 


C'OXFIDEXTIAL 



INDEX 


181 


pling coefficient; Hysteresis 
losses in transducers 
at resonance, 30, 53, 55, 56 
calculation from motional imped¬ 
ance, 27 
definition, 14 

effect of electromechanical coupling, 
58 

effect of termination, 57 

electromechanical, 393 

formula, general, 14-15, 17 

generalized transducer, 24 

high power level, 339 

IIP-3; 444 

mechanical, 393 

QC projector, 234 

radially vibrating, 139 

sample calculation, 20 

scanning system requirements, 370 

tube and plate, 223 

Efficiency of transducers, potential, 31 
admittance calculation, 53, 55 
impedance calculation, 55 
tube and plate element, 224 
variation with temperature, 103 

Elastic hysteresis, 65 

Electric analogues for transducers 
see Equivalent circuits for trans¬ 
ducers; Network equivalents, 
transducers 

Electrolytically cut laminations, 207 

Electromagnetic units, table, 3 

Electromechanical coupling coefficient, 
56, 58, 87, 393 
definition, 7 

for scanning transducers, 370 
variation with temperature, 101 

Electromechanical mutual impedance, 
transducer, 23 

Electromechanical networks, trans¬ 
ducers, 23-24 

Electronic switch (100 kc frequency), 
271 

Energy accompanying magnetostric¬ 
tion, 64 

Energy radiated by transducer, 
formula, 134-137 

Equivalent circuits for transducers, 57 
see also Network equivalent, trans¬ 
ducer 

loudspeaker, 25 

magnetostrictive transducers, 22-34 
radially vibrating transducer, 39-43 
ring transducer, 42 

hiquivalent mass, transducer element, 
393 

bar and piston, 181 
longitudinally vibrating bar, 177 
symmetrically closed multiple lami¬ 
nated bars, 182 

symmetrically closed multiple lami¬ 


nated bars with diaphragm, 183 
unsymmetrical closed multiple bars, 
185 

Facings, transducer 
aluminum, 419 
impregnated glass fiber, 412 
rubber, 377, 391 
synthetic coatings, 165 
Faraday’s law for induced emf, 1 
Fathometer transducer, 20 kc, 196-198 
Flux, definition, 1 
Flux density, definition, 2 
Flux meter, elementary, 1 
Formulas 

see also Network equivalent, trans¬ 
ducers 

acoustic power of transducer, 15 
admittance diagrams, 55 
dependence of Young’s modulus on 
magnetization, 7 

directivity patterns and directivity 
ratios, 105-138 

effective electromechanical coupling 
coefficient, 56, 57, 69 
efficiency at resonance, 55, 69 
Faraday’s, for induced emf, 1, 2, 3 
field within a solenoid, 1, 3 
impedance diagrams, 55 
magnetic susceptibility, definition, 2 
potential efficiency, 55 
Q of a mechanical system, 55 
radiation impedance of various 
sources, 134-137 

Rayleigh’s, reversible permeability. 
68 

resonant frequencies for various 
shapes, 177, 180, 182, 183 
sound intensity vs. pressure, 13 
strain vs. flux density, 5, 6 
threshold of a hydrophone, 14 
transducer efficiency, 15, 17 
velocity of sound wave, 13 
P'our terminal network, transducer, 23- 
24 

Fourier integrals for directivity pat¬ 
terns, 117 

Fourier series for directivity patterns, 
110 

Frequencies desirable for scanning sys¬ 
tems, 369 

P'requency, resonant 
laminated bar, 177 
laminated bar and piston, 180 
symmetrically closed multiple lami¬ 
nated bars, 182 

symmetrically closed multiple bars 
with diaphragm, 183 
Frequency doubler for impedance meas¬ 
urements, parabolic type, 2.56- 
257 


Frequenc}' doubling in high power 
transducers, 326 

Frequency response analyzer for trans¬ 
ducers, 315 

Frequency response measurements, 
transducer, 281-287 
Frequency response of transducer 
see Bandwidth of transducer, Q of 
transducer 

Frequeiicy standard ecpiipment for im¬ 
pedance measurements, 259-261 
Frictional resistance, transducer, 393 

Gaussian directivity patterns. 111, 117 
Gibbs’ thermodynamic potential, 63 

Hairpin shaped laminations, 221 
Half frequency driving current, 327 
Half hard annealing, 66 
Half-wave oscillators for testing mag- 
netostricive materials, 187 
Half-wave tube and plate transducers, 
225-236, 360, 419 

Harmonic injection in transducer driv¬ 
ing current, 328 
Harvard 6X6 projectors, 308 
Harvard Underwater Sound Labora¬ 
tory 

Ladderphone transducers, 197-199 
magnetostrictive properties of ferro¬ 
magnetic materials, 62 
tubular transducers, 146 
Heat treatment for transducer elements 
half-hard, 66 
hydrogen annealing, 66 
oxide annealing, 66 
partial annealing of hard nickel, 141 
ring stack laminations, 162 
High power driving of magnetostrictive 
transducers, 95, 217, 323-355, 
363 

High power level transducer imped¬ 
ance, 339 

History of magnetostrictive transducer 
research, 3-6, 9-11 
HP-2 transducer, 378, 431 
HP-2B transducer, 375, 434 
HP-3 transducer, 332, 377, 434-444 
HP-3DS transducers, 445 
HP-3S transducer, 438, 444 
HP-5 transducer, 377, 450 
HP-8D scanning transducer, 4.50 
H-RLP (ring ladderphone), 381 
HUSL admittance bridge, 252-255 
advantages and disadvantages, 249, 
2.50 

operation, 2.52-254 
HUSL impedance bridge, 246-252 
description of operation, 246-250 
evaluation, 249 

Hydrogen annealing of nickel, 66 


C'ONFIDENTIAI 





4«2 


INDEX 


llystereHis lo.sses in transducers 
definition, 3 

effect of lamination thickness, 351 
effect on response, 5 
measurement, (>7 
temperature dependence, 102 

1.1- IO transdvicer, 200 

1.1- 20 transducer, 200 
Impedance and admittance diagrams 

calculation of Q, 20 
geometrical relations, 49-51 
louds|)eaker, 25 

motional admittance circle, 393 
ring transducer, .52 
sensitivity calculation, 59 
summary of formulas, 55 
lmi)edance locus plotter 

description of circuit, 273-277 
possible improvement, 270-277 
Impedance measurement methods, 
transducer 

see also Impedance measuring equip¬ 
ment 

accuracy required, 237-239 
avoidance of air bubbles, 278 
bridge methods, discussion, 239-2()7 
bridge methods, jmlsed, 328-342 
deflection methods, 208-277 
high power level measurements, 339 
impedance vs. admittance calcula¬ 
tions, 54 

network methods, discussion, 200- 
208 

production tests, 427 
range and accuracy requirements, 
238-239 

reduction of bridge data, 2()4 
reflection errors, 279 
Impedance measuring equipment 
admittance bridge, portable, 280 
admittance locus plotter, 277 
admittometer, 209 
conductometer, 271 
fre(iuency-standard equipment, 259- 
201 

IIUSL admittance bridge, 252-255 
IIUSL impedance bridge, 240-252 
impedance locus plotter, 273-278 
impedometer, 208 

oscilloscope plotting methods, 273- 
278 

special frequency doubler, 250-257 
special oscillators, 255 
tuned detectore for bridge balancing, 
201-204 

vector re.solver circuit, 209-273 
W-10125 impedance bridge, 255 
Impedance quantities characteristic of 
t ransducers 
blocktHl impedance, 20 


Core imi)edance, 35 
electromecluinical mutual impedance, 
23 

frictional resistance, 393 
motional admittance, 51, .52 
motional impedance, 2.5, 29-30, 50 
motional reactance, 34 
mutual impedance, 00 
radiation impedance; see Radiation 
impedance 
total impedance, 27 
typical formulas and graphs, 31-33, 
39-42 

Impedometer, 208 
Intensity of magnetization, 02 
Intensity of souiul, definition, 13 
Inverse magnetostrictive effect, 40 
Iron-cobalt alloys, magnetostriction 
tests, 00, 77 

.lahnke and Kmde tables. 111 
.loide’s magnetostriction experiments, 
4, .5 

Ladderphone transducer, 197, 381 
Laminated bar stacks 
hair[)in-shai)ed, 221 
ladder type, 412 

multiple bars with diaphragm, 181- 
187, 194-221, 334-345 
ring-shaped ladder type, 414 
SP type, 411 

uniform bar with diaphragm, 170- 
181, 187-194, 301 
wedge-shai)ed type, 390 
Laminated ritig stacks, 101-109, 342- 
358, 390 

Laminated scrolls, 382 
Laminated tube hydrophones, 159-100 
Laminations 
bimetal, 402 
consolidation, 425 
elect rolytically cut, 207 
preparation, 424 

Latex rubber for coating transducers, 
10.5 

Line source bookphone, 190 
Line source directivity patterns, 113- 
119 

Linearity of transducers, discussion, 
323 

Loading of transducer 

see Acoustic loading; Radiation im¬ 
pedance 

Longitudinally vibrating transducer 
theory, 44-49 

Longitudinally vibrating transducers 
see Magnetostrictive elements, longi¬ 
tudinally vibrating 
Losses in transducers 

see Eddy current losses in trans¬ 


ducers, Hysteresis losses in 
transducers 

Loudspeaker, impedance diagram, 25 
Loudspeaker, network equivalent, 24, 
28-29 

Loudspeaker, underwater, 145 

M-.5 transducer, 173 
Magnesium faces for transducer ele¬ 
ments, 419 

Magnetic circuits in tapered laminated 
stacks, 401-411 

Magnetic domains, de.scription, 1 
Magnetic field, definition, 1 
Magnetic flux, definition, 1, 2 
Magnetic induction, definition, 1 
Magnetic measurements 
see Magnetostrictive materials 
Magnetic moment per unit volume, 
formula, 2 

Magnetization curves at high temper¬ 
atures, 79, 80 
Magnetocaloric effect, 04 
Magnetomechanical formulas, 62 
Magnetostriction 
de.scription, 3 
force available, 8 
history of research, 3-0, 9-11 
hysteresis effect, 5 
inverse, 4 

measurements, 5, 79 
Magnetostriction constant, 0, 38, 44, 03 
measurement, 89 
variation with temperature, 104 
Magnetostrictive elements, longitudi¬ 
nally vibrating 
see also name of design 
future dev'elopments, 360 
hairpin-shai)ed laminations, 221-222 
multiple bar and piston lamination 
types, 181-187, 194-221, 333- 
342, 411-414 

ring-shaped ladder, 414-416 
T-shaped laminations, 191-193 
tube and cone, 224 
tube and cylinder, 223 
tube and plate designs, 22.5-230, 360, 
410-422 

uniform bar and piston laminations, 
170-181, 187-194, 300 
wedge-shaped laminations, 396-411 
Magnetostrictive elements, radially vi¬ 
brating 

see also name of design 
corrugated tubes, 395 
cylindrical tubes, 140-151, 359, 395 
internally-radiating rings, 171-175 
laminated ring stacks, 101-109, 342- 
355, 358-360, 396 


CONFIDENTIAL 



INDEX 


laminated tubes, 159-160 
ring scrolls and spirally-wound tubes, 
160-161, 173, 359-361 
toroidal tubes, 143 
tubular arches, 395 
tubular arrays, 146, 169-171 
Magnetos!rictive materials 
cold working effects, 356 
criteria for selection, 65, 95, 100 
dynamic measurements of proper¬ 
ties, 69, 84 
electroplating, 357 
heat treatment, 66, 356 
ideal characteristics, 356 
iron cobalt alloys, 65, 77, 88, 89 
magnetostrictive formulas, 62 
nickel and nickel alloys, 65, 70, 71, 89 
sintered powders, 356 
static measurement of properties, 68, 
79 

vicalloys, 79, 91 

Magnetostrictive stress, maximum 
usable, 9 

Magnetostrictive transducers 
as electrical networks, 22-34 
definitions of characteristic proper¬ 
ties, 13-17 

history and survey, 1-21 
summary of types, 11-13 
Magnetostrictive transducers, general 
types 

see also under name of type 
assymetrical stacks, 202-207 
bookphone, 187-191, 360 
depth-angle transducers, 219-221, 
445 

high-power types, 323-355 
HP transducere, 376, 431-450 
ladderphone, 197, 381 
laminated tubes, 159-160 
longitudinally vibrating types, 176- 
236, 333-416 

multiple bar and piston laminations, 
181-187, 194-221, 333-342 
nickel stacks, 166 
Permendur-2V stacks, 167 
QC projectors, 230-236 
radially vibrating types, 139-175 
ring scrolls, 160-161, 173 
ring stacks, 161-169, 342-358, 395 
ring-shaped ladder, 414-416 
scanning types, 366-422 
sonic listening hydrophones, 141 
SP type stacks, 411 
SPEP transducers, 210-219, 332 
stepped-frequency, 208-210 
tube and cone, 11, 224, 225 
tube and cylinder, 223 
tube and plate, 225-236, 360, 416- 
422 

tubular arch, 395 


tubular hydrophones, 140-151, 169- 
171 

wedge-shaped stacks, 396-411 
wide-hand, 171, 208-210, 224 
Magnetostrictive transducers, specific 
models 

B-6A hydrophone, 148 
B-6B hydrophone, 150 
B-6C hydrophone, 148 
B-19 hydrophone, 150 
B-19A hydrophone, 150 
B-19B hydrophone, 148-151, 154, 
310 

B-19II hydrophone, 154-156, 310, 
382 

B-19H midget hydrophone, 156 

B-19K hydrophone, 156 

B-19L hydrophone, 156 

CI-50; 200 

CI-60; 200 

CI-61; 200 

CI-63; 200 

CI-64; 200 

CI-65; 200 

CI-100; 194 

HP-2; 378, 431 

HP-2B; 376, 434 

HP-3; 332, 377, 434-444 

HP-3DS, 445 

HP-3S, 438, 444 

HP-5; 377, 450 

HP-8D, 450 

IJ-10; 200 

IJ-20; 200 

line source bookphone, 190 
M-5; 173 

MKX hydrophone (BTL), 161 

MOX, 193 

XL-124; 144 

NL-130; 144 

QCL projector, 230, 235 

QCU projector, 234, 235 

QGA projector, 235 

QP projector, 170 

ring ladderphone, 381 

SP-1; 379 

20-kc fathometer transducer (Sub. 

Sig. Co.), 196 
XI-10; 232 
XI-15; 232 
XI-20; 232 
XI-30; 232 
XI-40; 232 
XI-50; 232 
XI-60; 232 
XI-100; 234, 235 
XJ-20; 232 
XJ-30; 232 
XJ-40; 232 

Magnets, polarization and aging, 151 


483 


Materials for transducer mountings, 
373 

Materials survey, magnetostrictive, 62- 
104 

Mechanomotive force, 59 
Millerphone transducer assembly, 380 
Minor hysteresis loop, 68, 97 
MKX hydrophone, 161 
Motional admittance, transducer, 51, 
393 

Motional impedance, loudspeaker, 25 
Motional impedance, transducer, 29- 
30, 50 

Motional reactance, transducer, 34 
Mountings for transducers 

see Assembly and mounting of trans¬ 
ducers 

MOX transducer, 193 
Mutual impedance, transducer, 23, 59 
60 

Naval Research Laboratory, 12 
Neoprene paint for coating transducers, 
165 

Network equivalent, loudspeaker 
four terminal, 23-24, 28-29 
two terminal, 25 

Network equivalent, transducer, 22-34 
see also Equivalent circuits for trans¬ 
ducers 

band-pass filter, 56 
electromechanical network, 23-24 
mass loaded rod, 47 
mechanical losses in a rod, 49 
reciprocity theorem, 22, 23 
rod with one free end, 46 
six terminal, 45 
T networks, 23, 191, 266-268 
New London Laboratory 
thimble hydrophones, 169 
tubular hydrophones, 140, 143, 145 
Nickel, properties 

see A nickel, properties; D nickel, 
properties; Z nickel, properties 
9X9 inch assymetrical stack trans¬ 
ducer, 202-207 

Noise generators for transducer meas¬ 
urements, 315 

Noise signals, effect on directivity pat¬ 
terns, 130 

Non-linear operation of transducers, 
323-355 

Normal magnetization curve, 2, 62 

Oil filling of transducers 
HP-2B, 434 
ring stacks, 163 
scanning transducers, 438 
Open-circuit sensitivity, transducer, 296 
Oscillators for impedance bridge meas¬ 
urements, 255 


CONFIDENTIAL 



48i 


INDEX 


Oscilloscope plotting of transducer im¬ 
pedances, 273-277 
Oxide annealing of nickel, ()6 

Permalloy-45 
composition, 65 

dependence of remanence on anneal¬ 
ing temperature, 79 
resistivity, 93 

Young’s modulus when magnetized, 
93 

Permanent magnet materials, 357 
Permanent magnet polarization of 
wedge-shaped stacks, 402-406 
Permeability 
at constant strain, 64 
at constant stress, 64 
calculated from impedance data, 84 
curve for nickel, 6 
incremental, 38 
reversible, de6nition, 7 
static, definition, 7 
temperature variation, 102 
Permendur laminations, wedge shaped, 
405 

Permendur stack, at high power level, 
342 

Permendur-2V 
composition, 66 

dependence of remanence on anneal¬ 
ing temperature, 79 
magnetic characteristics, 405 
normal magnetization curve, 79 
resistivity, 93 

Young’s modulus when magnetized, 
93 

Phase differences between transducer 
elements, 367 

Phase patterns of transducer, 105 
Phasing of point sources in transducer, 
109, 112 

Phenol-formaldehyde compound for 
casting tubes and ring stacks, 
144, 165 

Pitometer Log hydrophone, 157 
Plastic faces for transducer elements, 
378, 419 

Plastics for consolidating transducers 
cast-in-plastic ring stacks, 165 
cast-in-plastic tubes, 144 
Point source arrays, directivity pat¬ 
terns, 106, 110, 112 
Polarization, transducer 
by permanent magnet, 150 
laminated bar, 177-179 
laminated stacks, 429 
tube and plate transducers, 236 
wedge-shaped laminated stacks, 401- 
411 

Portable polar chart recorder (PPCR), 
317 


Portable transducer measuring equip¬ 
ment, 280 

Potential efficiency of transducers 
see Efficiency of transducei's, poten¬ 
tial 

Power output of transducer, ultimate 
limit, 326 

Power requirements for scanning trans¬ 
ducers, 370 

Pressure, maximum obtainable from 
magnetostriction, 9, 374 
Pressure-release materials, 363 
Pressure-release screens, 322 
Product theorem for line sources, 115 
Product theorem for surface sources, 
125 

Pulsed impedance bridge measure¬ 
ments, 328-342 

Q of a mechanical system, 29, 55 
Q of transducer 

see also Bandwidth of transducer 
bar and piston, 181 
determination from response curve, 
21 

effect on efficiency, 395 
mechanical Q, 56 

motional impedance calculation, 26 
multiple bar types, 177, 182, 183, 185 
QC projector, 236 
radially vibrating transducer, 139 
ring stack, 161 
tube and plate, 417 
QC transducers 

see Tube and plate transducers 
QCL projectors, 230, 235 
QCr projectors, 234, 235 
QGA projectors, 235 
QP projectors, 170, 310 

Radial transducer theory, 39-44 
efficiency, 43 
electrical impedance, 40 
equivalent electrical circuits, 42 
impedance diagrams, 49 
maximum efficiency, 43 
mechanical impedance, 39 
motional admittance, 51 
mutual impedance, 40 
resonant frequency, 43 
Radially vibrating transducers, 140- 
175, 342-396 

see also Magnetostrictive elements, 
radially vibrating 
acoustic loading, 140 
efficiency, 139 
general characteristics, 139 
Radiation impedance 
circular piston, 136 
cylinder, 136 
cylindrical dipole, 136 


dipole sphere, 136 

flat strip, 137 

in terms of efficiency, 393 

laminated bar, 177 

laminated bar and piston, 181 

of air, 28 

of water, 30 

specific radiation admittance, def., 
136 

specific radiation impedance, def., 
135 

sphere, 136 
Radiation patterns 

see Directivity patterns, theoretical 
Radio sono buoy hydrophones, 142 
Rayleigh’s reversible permeability 
formula, 68 
Receiving patterns 

see Directivity patterns, theoretical 
Receiving response 

see Sensitivity of transducers 
Reciprocity calibration of transducers, 
17-18, 311-313 

Reciprocity parameter, 16, 312 
Reciprocity theorem, 15-16, 22-23, 59, 
105-106 

Recommendations for future research 
see also Chapter Li 
high power driving methods, 355 
investigation of short pulse tech¬ 
niques, 324 

use of harmonics in driving high 
power transducers, 328 
Recorders for sound level, 307 
Rectangular source, directivity pattern, 
125 

Reflection errors in transducer testing, 
279 

Reflections due to improper transducer 
mounting, 362 

Release baffle, definition, 120 
Remanence, definition, 3 
Remanence-operated transducers, 75, 
96, 141, 148 

Resinox for coating transducers, 144, 
166 

Resistance, acoustic (def.), 13 
Resistivity of magnetic materials, vari¬ 
ation with temperature, 102 
Resistivity measurements, 69 
Resolver circuits, 269-273 
Resonance of radially vibrating trans¬ 
ducer, 139 

Resonant frequency of wedge-shaped 
laminations, 399 

Response curve determination, 295 
Retentivity, definition, 3 
Reversible permeability, definition, 6, 7, 
64, 68 

Reversible permeability of sintered ox¬ 
ide magnets, 408 


CONFIDENTIAL 



INDEX 


485 


Ring laclderphone, 381 
Ring scroll transducers, 160-161, 173 
Ring shaped ladder type laminations, 
414-416 

Ring source (cylindrical shell) 
electrical impedance formulas, 39-42 
radiation impedance, 136 
Ring stack transducers, 161-169 
bonding, 162 
cast-in-plastic, 165 
design, 161 
edgewise wouml, 396 
half hard nickel, 167 
heat treatment of laminations, 162 
high power level, 342-355 
internally radiating, 172-175 
M-5; 173 

maximum power output, 327 
mountings, 164, 358 
non-directional ring stacks, 168 
oil filling, 163 
(jue-turn winding, 358 
Q, 161, 358 

radiation patterns, 174 
scanning, 393, 396 
segmented, 358 
thin walled stack, 166 
2V Permendur stack, 166 
windings, 162, 173 
Rod and plate transducer 
see Tube and plate transducers 
Rod transducer, theory 
see Tube transducer, theory 
Rubber “boots” for transducers, 392 
Rubber facings for transducers, 377, 431 

Sangamo HP5 transducers, 377, 450 
Saturation, magnetic, 3 
Scanning transducer design 
see also Ti'ansducer theory 
accuracy of element placement, 375 
active face design, 374-375 
assembly of elements, 430-439 
beam rotation method, 366 
cables, 390 
cavitation, 374 
construction, 423 
cost, 362 

design and assembly factors affecting 
beam patterns, 365-370 
efficiency and power requirements, 
370 

frequency selection, 369 
future development, 359-362 
lamination design, 396-401 
maximum efficiency, 393 
mechanical requirements, 370 
mounting sui)ports, 371 
non-cii'cular, 362 
pattern requirements, 365-370 


performance tests, 439 
phase shifts, 367 
plastic faced, 378 
polarization, 401-411 
rubber faced, 377 
shape of elements, 376 
size of transducer, 369 
streamlined, 362, 392 
submarine types, 362 
terminal box and cable seals, 384- 
390 

testing, 427, 439 
types of elements, 375, 393-422 
Sensitivity of transducers 
B-19H hydrophone, 153 
impedance diagram calculation, 59 
open-circuit (voltage) sensitivity, 
definition, 14, 292 

receiving and transmitting re¬ 
sponses, 14, 17 

short-circuit (current) sensitivity, 
definition, 14 
tube and cone, 224 
Shaded arrays 

9X9 inch laminated stack, 203 
SPEP transducers, 210-219 
Shaded transducer patterns, 108, 115 
Shock resistance, B-19B hydroi)hone, 
153 

Sintered oxide magnets, characteristics, 
405 

Six terminal networks, transducers, 45 
Sonic listening hydrophones 
see also Tubular hydrophones 
directivity index, 141 
noise discrimination, 141 
sensitivity, 141 

Sound field measurement, 293 
Sound gear monitor, calibration pro¬ 
cedure, 319 

Sound gear monitor, hydrophone, 146- 
159 

Sound intensity, definition, 13 
Sound velocity 
formula, 13 
in nickel, 399 
in water, 321 

SP type laminated stacks, 411 
SP-1 transducer, 379 
Specific radiation admittance, 136 
Specific radiation impedance, 135 
SPEP transducers, 210-219, 332 

acoustic and electric ijerformance, 
212 

direct current polarized models, 210- 
214 

directivity patterns, 212 
high power level ])erformance, 217, 
333 

impedance measurements, 214-219 
laminations, 211 


permanent magnet polarized models, 
214 

shaded windings, 211 
sword arm depth angle transducer, 
219-221 

Spherical source 

radiation impedance, 136 
ring stack, 168 

Spiral-wound tube transducer elements, 
160, 173, 358 

Spool assembly of transducers, 435 
Spy Pond transducer test station, 289 
electronic equipment, 297-308 
Square radiator, directivity patterns, 
127 

Standard frequency equipment, 259- 
261 

Standard hydrophones, 308 
Static magnetostriction 

measurements on iron-cobalt rods, 79 
measurements on nickel, 79 
research history, 3 
Static permeability, definition, 3 
Stepped-frequency transducers, 208- 
210 

Strain, magnetosfrictive, 83 
Strain demagnetization, 98 
Strain vs. flux density, formula, 5 
Streamlining scanning transducers, 362, 
3‘)2 

Strength of a ])oint source, definition, 
105 

Stress formulas, magnetostrictive, 38 
Stre.ss from magnetizing a clamped 
rod, 8 

Submarine scanning transducer types, 
362 

Submarine Signal Company, 20-kc 
fathometer tran.sducer, 196 
Support materials for transducers, 373 
Surface sources, radiating conditions, 
119 

Susceptibility, definition, 2 
Sword arm depth angle transducer, 
219-221 


T networks, transducer, 23, 191, 266- 
268 

Tanks for transducer testing, ab¬ 
sorbent-lined, 281 

Temperature effects in magnetostric¬ 
tion, 101-104 

Terminal box seals, transducer, 384 

Termination of transducer, effect on 
efficiency, 57 

Test facilities at HUSL 
Charles River barge, 288 
Spy Pond station, 289 
Tippecanoe, 288 
USS Galaxy, 288 


CONFIDENTIAL 




186 


INDEX 


Theory of magnetostricfive transducers 
see Transducer theory 
“Thimtde” hydrophones, 169 
Threshold of hydrophone, definition, 14 
“Tippecanoe”, transducer test barge, 
289 

Tolerances in transducer assembly, 367, 
375 

Toroidal tube transducer elements, 143 
Transducer assembly and mounting 
see Assembly and mounting of trans¬ 
ducers 

Transducer coupling coefficients 

see Electromechanical coupling co¬ 
efficient 

Transducer design, scanning 
see Scanning transducer design 
Transducer efficiency and losses 

see Eddy current losses in trans¬ 
ducers; Efficiency of trans¬ 
ducers; Hysteresis losses in 
transducers 

Transducer elements and arrays, mag- 
netostrictive 

see Magnetostrictive elements, lon¬ 
gitudinally vibrating; Magne¬ 
tostrictive elements, radially 
vibrating 

also see under name of type 
Transducer frequency response 

see Bandwidth of transducer; Q of 
transducer 

Transducer impedances 

see Impedance, Radiation impedance 
Transducer network equivalents 
see Network equivalent, transducer 
Transducer termination, effect on effi¬ 
ciency, 57 
Transducer tests 
see Impedance measurement 
Transducer theory 

see also Scanning transducer design 
calibration theory, 311 
designing for desired pattern, 117 
directivity pattern prediction, 111 
effective area of, 60 
efficiency at resonance, 30 
equivalent electrical circuits, 22-34 
longitudinally vibrating transducers, 
44-49 

loudspeaker as example, 24 

motional impedance, 31 

motional reactance, 34 

maximum power outi)ut, 100 

noise, 14 

optimum Q, 99 

potential efficiency, 31 

radially vibrating transducers, 39-44 

reciprocity, 15, 17-18 

sensitivity, 14 

shading methods, 115 


tubular transducer theory, 44-49 
Transducer types, magnetostrictive 
see Magnetostrictive transducei's, 
general types; Magnetostrictive 
transducers, specific models 
see also under name of type 
Transmitting patterns 

see Directivity patterns, theoretical 
Transmitting response 
definition, 292 

relation to receiving response, 17 
Transmitting response curve, 295 
T-shaped laminated elements, 191-193 
Tube and cone transducers, 11 224 
Tube and cylinder transducers, 223 
Tube and plate transducers, 223-236, 
416-422 

comparison, 234 
early model, 223 
four-tube hydrophone, 225 
future development, 360 
magnesium plate, 234, 419 
magnetic circuit, 236 
millerphone, 380 
QC’ projector, 230-236 
scanning, 378, 393, 416-422 
tube and slotted-plate projector, 228 
wedge-shaped plate, 420 
Tube and plate transducer elements 
QC-like type, 416-419 
Tube transducer theory, 44-49 

equivalent circuit for a mass loaded 
rod, 47 

equivalent circuit for a rod with one 
free end, 46 

equivalent network, six terminal, 44, 
45 

internal mechanical losses, 49 
Tubular arch transducer element, 395 
Tubular element transducer arrays 
B-19II, (QP), 170 
design considerations, 381, 395 
four tube, 146 
ten element, 170 
twenty-eight element, 169 
Tubular hydrophones 
B-6 hj'drophones, 150 
B-19 hydrophones, 150 
B-19B, 150-154 
B-19H, 154-156 
B-19II midget, 156 
B-19K, 156 
B-19L, 156 
cast in plastic, 143 
early types, 146-151 
Harvard models, 146 
installed SGM, 157 
laminated tube, 159 
NL-124; 144 
NL-130; 144 
I'adio sono buoy, 142 


requirements, 141 
sonic listening, 141, 143-146 
“thimble” hydrophone, 169 
underwater loudspeaker, 145 
Tuning, electrical 

tube and plate hydrophone, 225 
Tuning, mechanical 

stagger-tuned laminated stacks, 209 
tube and jjlate element, 223 
tube and plate hydrophone, 225 
“Turk’s-head”, 445 
20 kc fathometer transducer, 196-198 
Two terminal networks, transducer, 25 

Underwater loud speaker, 145 
Uniform bar transducer elements, 176- 
179, 187 

I'niform bars with pistons, 179-181, 
187-194 

Units, electromagnetic, 3 

Vectolite (sintered powder magnet ma¬ 
terial), 358 

Vector admittance locus plotter, 277 
Vector impedance locus plotter 
descrii)tion of circuit, 273-277 
possible improvement, 276-277 
Vector resolving circuits, 269-273 
Velocity of sound 
formula, 13 
in nickel, 399 
in water, 321 
Vicalloy-0.5V 
composition, 66 
resistivity, 93 
revereible permeability, 79 
Young’s modulus when magnetized, 
93 

Vinylseal cement for consolidating 
transducers, 66 

Voltage analogues of velocity, 57 
Voltage level recorders, 307 
Voltage transmitting response, pro¬ 
jector, 296 

Water, radiation impedance, 30 
Water seals for transducers, 361, 384, 
436 

Wave number (acoustic), 108 
Wedge-shaped laminated stacks, 396- 
411 

Wedge-type plate and tube transducer 
element, 420 

Wide band transducers, 171, 208-210, 
225 

Winding methods for laminated stacks, 
428 

XI-10 projector, 232 
XI-15 projector, 232 
XI-20 projector, 232 
XI-30 projector, 233 


CONFIDENTIAL 



INDEX 


487 


XI-40 projector, 234 
XI-50 projector, 234 
Xl-60 projector, 233 
XI-100 projector, 231, 234 
X.J-20 projector, 232 
XJ-30 projector, 233 
X.I-40 projector, 234 


Yoiiiig’s modulus, isothermal and adi¬ 
abatic, 64 

Young’s modulus for magnetized ma¬ 
terial 

calculated from impedance data, 91 
dependence on H, 7 
nickel, 93 

variation with temperature, 103 
with polarizing flux, formula, 38 


Z nickel, properties 

magnetostrictive constant, 90 
maximum coercive force, 75 
resistivity, 93 
reversible permeability, 75 
Young’s modulus when magnetized, 
93 


(’ONFIDENTIAL 




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Hi.* 




















































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































